Well MarkT, I have news to report.  I removed the fuel tank today to re-check all the wiring underneath and the very first thing I saw was a rather "melted" and somewhat deformed looking rectifier.  I connected the battery to the bike and within a few seconds, the rectifier was HOT to the touch. At this point, I disconnected the rectifier and reinstalled my old one.  There was then no hot or warm wiring whatsoever and the rectifier also remained cool to the touch (bike was not running in any of these scenarios). 
OK...was this a fatal case of "If it ain't broke, don't fix it" on my part?  As I said in an earlier post, because I wasn't 100% sure of how to properly test a rectifier, I went ahead and ordered & installed the new one.  I bought it from this eBay seller:

The part number matches the part number that my bike supposedly takes, so I thought I was good to go, but now I notice that in the seller's drop down menus of compatible bikes, the '75 DT250 is NOT listed!  Confusing, to say the least.  So that's where I'm at right now.  But I do have a few questions:
1.  Can someone tell me the proper way to test my old rectifier?  I do have a multi-meter.  I'm just unsure as to how to properly test a rectifier.
2.  It's my understanding that the rectifier converts AC current to DC for the lighting.  My biggest worry is that if mine is bad, I will somehow blow all the bulbs I just replaced.  I DO have a voltage regulator installed per Yamaha's service advisory.  Will a faulty rectifier lead to blown bulbs or just no lights at all?
3.  Finally, can anyone suggest a reputable source from which to purchase a new rectifier?
Thanks again for all your help guys.  This thing has literally been kicking my (mental) ass these past few weeks, and I really am anxious to get it on the road (and trail)!

Take more notice of Mark than 'me' as i get a bit lost haha. But does sound like rectifier was shot as i think Mark suggested, so i guess the charging coil was connected to the battery due to 'that' rectifier fault. Unless you had the rectifier connected back to front which wouldn't be easy to do so probably not. So the coil became that big heat sink resistance & i don't think that goes through the switch??--anyone. Talking back to front--i guess your battery is connected negative to earth as it should be. Sorry--had to ask.

I would guess the rectifier is not doing its job or it is hooked up backwards.

How to check a rectifier or diode.... - Vintage Enduro Discussions (yamaha-enduros.com)

I have the rectifier connected with the red wire going to the "+" symbol and the white wire going to the "~" symbol. 
The seller of the rectifier wrote me the following:"Even if faulty, the rectifier would not make the battery lead get hot. An overloaded circuit or short would pull enough current to melt the rectifier."

Received this message from the eBay seller that sold me the rectifier this morning.  I'm going to test my old rectifier as well as the charging output on my bike later today (hopefully)."I don't know how well the rectifier would function after it melted. The easiest test would be to test the charging voltage when the bike is running. Your rectifier isn't working if the voltage does not change (burned out) or if the output voltage is AC (internally shorted). I'm guessing that this one fried internally and might be the latter.

Inside a half-wave rectifier there is only 1 part, a diode. It should let voltage pass through one way and not the other. For simple instructions those look overly complicated. - Set the meter to diode mode and put the red lead on the ~ and the black lead on +. It should beep and read around half a volt (reading depends on the meter). Switch the leads and it should read nothing. A full wave rectifier tests similar, only there are 4 diodes to test.

I can send you a replacement part, but I think that I'll send the aluminum housing "heavy duty" version just to be safe.
Does that work for you or would you rather have the plastic one? The parts fiche that you sent me has the aluminum housing in the breakdown photo but the plastic one in the description."

Sounds to me like one really righteous dude.

Most common reasons for rectifier diode to break are:

Installed backwards

Someone hooked up the battery backwards (even for a split second)

Someone hooked up battery charger backwards (even for a split second)

If if was installed backwards, it's usually toast.  It will turn into an "open circuit" within a couple seconds usually.

A quick "reverse polarity" connection can blow out the diode to where it still makes a connection but loses the ability to be a one-way valve.  This will allow AC to the battery and will sometimes fry the battery.  Damaged diode will also allow battery to drain through stator coils which can fry the the stator.

Thank you Mark T... this explains things I keep wondering about... 
Sneezles61

Thanks for that information MarkT. 
I know I installed the rectifier correctly, as I connected it the same way as the old one and confirmed that connection here in the forum (red wire to the "+" symbol side and white wire to the "~" symbol side).  I can't imagine ever connecting the battery backwards, as the positive lead and wire from the harness is bright red and the negative lead and ground wire from the harness are both black.  The Battery Tender would also be hard to imagine connecting backward for the same reason.  I tested the rectifier the gentleman sold me today (with 3 separate multi-meters) and all showed it was bad.  It tested as an open switch in both directions.  When I tested my old rectifier the same way, it showed that it was fine...."OL" in one direction and about .457 volts in the other.  One thing that still bothers me Mark, is that connection you told me to make when I installed the '77 stator where you said to just connect BOTH the "green-white" and "green-red" from my harness to the solid green on the '77 stator (the only green it has).  The thing that has me confused is when I look at the attached photo (part of the wiring diagram for my bike) and see that the "green-white" and "green-red"...when connected with the WHITE in the lighting switch, appear to do the exact opposite of each other.  Maybe I don't know how to read a wiring diagram, but doesn't this image indicate that when WHITE and "Green-White" connect it means the lights are OFF and when WHITE and "Green-Red" connect the lights are ON?  Again...maybe I'm way off base here, but if not....how can the green-white and green-red be connected to each other if they accomplish the opposite thing?  Thanks again for your help Mark! 

Okay...  go back and read what I've written at least a couple times.  What do the green wires have to do with lights?  Answer NOTHING.  They charge the battery.

Cut the green wires and all the lights will work...  at least until the battery runs dead. LOL

Once again, the early bikes had two "battery charge rates".  Like a battery charger with a switch that lets you select 1 amp output or 2 amp output.  In daytime mode which is lights off, the battery charge current is different than when the switch is in night mode with lights on.  And again, this is all explained in the manuals.

 

On the later models like the one you took the ignition from, Yamaha went to a single green wire and got away from "day and night" charging.  Battery charges at the same rate all the time. That's the difference.  That and I'm pretty sure you MUST run a regulator with the later model system.

If it makes you feel any better, tape off both green wires in your harness.  Disconnect the white wire at the rectifier and tape it off.  Now take the single green wire coming out of your stator and connect it to a length of white wire and connect that to the white wire (~, S on its side) side of the rectifier bypassing the handlebar "charge select" switch completely.  Now the AC from the stator green will get turned to DC by the rectifier and charge the battery when engine is running.  Which is how the later bikes with only one green wire at stator are wired.

P.S.  If you haven't figured it out, moving the light on-off switch on the handlebar on your original bike is like operating three completely separate switches.   One switch connects the headlight to AC from the stator, One switch connects the battery to the taillight, and one switch selects the battery charge rate. All controlled from moving the one on-off slider.