After tying the lever overnight, the next day I try pushing bike back and forth in gear (engine off of course).  If that doesn't break it free then riding with lever pulled might... 

With the water intrusion you've spoken about it's a long shot but worth a try.
Fingers crossed!

Does the $300 engine have its oil pump please? 

I believe the engine does have the oiler. I can post the link if you want. The engine looks pretty neglected, but it's probably worth it in parts.

Well, the cheater method for getting the clutch unstuck didn't work. Looks like I'm going to dig into the clutch after all. Not a big deal, I knew I was eventually going to anyways. Also, the carb floats need to be set. It sat overnight and flooded the engine.
On the plus side, I got it roll-started in 1st gear and rode it up and down the cul-de-sac a couple times. It seems like it has plenty of get-up-and-go! It wanted to wheelie in first gear. Does anyone have any tips and tricks for removing the clutch? Do I need a special tool? Does anyone have a good video that they recommend? I've rebuilt a couple motorcycle clutches before, but it seems like they all have their own quirks. I will get started draining the oil soon and getting ready to pull the side cover.

No special tools to get it "unstuck".  When you want/need to remove the basket you'll need a proper tool to hold the inner hub. 

Oh, always turn the petcock off.  The older bikes float valves never sealed perfectly and flooding was common if petcock was left on.

I did turn the petcock off, but I think that it needs to be rebuilt. Didn't really seem like it did its job.
It's a good thing I pulled the cover! That engine is nasty inside. There's so much aluminum corrosion and debris. There was also no way that clutch was going to free up on its own. It looks like the plates are pitted and rusty.
imgur.com/a/sDPV7c5
I'm in the process of removing it now. Maybe I will get lucky and just sand down the plates, but I doubt it. More likely a total rebuild is in order.

Well, the water intrusion was definitely the issue. First picture shows the clutch disks frozen together, second shows the disks pried apart. We'll see if sandpaper helps, but I doubt it! They're pretty far gone. This is the worst clutch I've ever dealt with.
imgur.com/a/PPJOrVG

good morning Mr Super Crusty,

1. clutch needs a tool to hold it - yambits have them
yambits.co.uk/dt250-clutch-holding-tool-p-4459.html
you may find that removing the plates, o-rings and cleaning it up is enough.

2. please post that engine link - TIA

cheers
Dave

Well, I got the bike to ride and it seems like the clutch is working OK. I sanded down the rusty clutch disks and cleaned off the friction plates. I rode it around the block, but it will not go into any gear higher than 2nd. I guess I have to pull the engine apart again. Any ideas why the bike won't shift higher? When I get time this week I will see if it goes into 3rd without a load on the wheels.
Also, here's the link. The guy also has an RT360 engine for sale. Both of them look pretty rough. spokane.craigslist.org/mpo/d/spokane-yam...ines/7760387061.html

My… there’s plenty of engine to have for 300.00!