Ok fellas, here is an update with videos. My phone camera is on selfie mode, so everything is ass backwards.  I disassembled the carb and put it thru several cycles in the ultrasonic cleaner. I probed everything to ensure the passages were clear, including that tiny one in the bottom of the bowl. I made some minor cable adjustments and made sure the slide was coming fully down and raising fully up. I inserted the idle speed screw and saw that it appears to interface with the slide ramp properly. I did clean up the slide ramp surface to smooth out those two indentations, but they really weren’t as bad as they looked in the magnified camera photo I had previously shared. I did remove the o-ring from the idle speed screw.

This first video is simply showing a start up and idle for your trained ears to give opinions. lol 


This second video is simply for your trained ears to hear it idle for a bit. And you will see that I had to remove the spring from the idle speed screw because the spring went solid before the screw could obtain the proper idle speed.


This third video is for your trained ears to go along for a ride. My phone is simply clipped to my jacket, so it is aimed at nothing in particular. Now remember that I had to remove the spring in order to get the idle speed screw threaded in far enough to obtain the proper idle….. Well notice how the engines dies as soon as I pull up to the garage. That spring was there for a reason…..


This fourth and final video was taken so you can see how the idle is still erratic in that it first settles at about 3k and then slowly sneaks into the lower RPMs where it will occasionally stall, just like it did before I tried all this crap. Luckily I had obtained a China carb with the original purchase of my 175B. I never used the China carb because I found a nice original carb at a fair price. So I borrowed the idle speed screw from the China carb to replace the one I LOST DURING MY TEST RIDE!!!


So I am open to any comments or suggestions after allowing your trained ears to suffer thru a bunch of boring amateur videos.

Could try the chinese carb it came with. I would if it's new. [sorry, wash my mouth out].
My trained [deaf] ears thaught they detected left main bearing play which leads me to the left crank seal.
I'm the last one to blame seals as never had leaking ones but have had them blow out with instant results.
Just grab the mag nut & see if any up & down play.
Motor sounds lively & my painted on ears thought they heard clutch slip when you hit third gear.
That's totaly irrelevant to the erratic idling problem so 'shut up me'.
One more go--have you got the ignition close to 1.8mm btdc.
Just thinking if its too advanced it might contribute to not wanting to drop down to idle & hang on for a bit.
That's me clutching at straws though.
Swap the carb & check the left main for feel.

Thanks Morley, I will check all your suspicions. The China carb was purchased by the PO of my 175B and never used. It can't hurt to give it try on this 175C. And yes the clutch is slipping a bit. I have new frictions ready to install. They sent me the wrong ones when I ordered them for my CT1B and MarkT helped me determine that they measured correct fit this 1976 engine. 
Stay tuned for further developments. 

Schu, that's a bugger losing the idle screw.
Had the same thing with the ignition key on The Greenie dropping out, I managed to find it about 200 yards from home.
Sounded good before with just the idle screw, are you sure the screw and spring are correct for the bike?

Yes I compared the original (lost) screw to the one on my 1975 and they were identical as stated in the Yamaha parts diagrams for 75 and 76 models. Luckily I had also compared it to the China carb screw and it was the exact same length. The only noticeable difference is that the China screw is zinc coated steel where the original was bronze. I will eventually swap out the China screw once I get my hands on another original Yamaha screw.

Oh my....
Morley I just pulled the side cover so I could grab the flywheel and check for bearing slop. As soon as I loosened the cover oil came pouring out. I just rode the bike prior to removing the cover. How can it run when the flywheel is spinning in an oil bath? Well it looks like i have something to do this weekend.... but at least there is no movement from bearing slop.

I'm more than happy to be wrong.
Oil needs tracking down.
Is it real oil or leaking crank seal & fuel has evapourated leaving oil.
Sounds like a lot of oil from what you say.
If it's taken forever to acumulate it might be minor, but then again does it point to an airleak affecting idle things. Surprised it's CDI has someone replaced the entire system prior to your ownership.
Oil doesnt worry points within reason though.
Getting 'very' interesting.

I assumed it was CDI but it’s not. And it was a considerable amount of oil. Like maybe 10 table spoons.

It just keeps getting better.  Apparently the PO didn’t have JIS bits for his impact tool. So it appears that he just beat the crap out of it with some sharp object.

Decision decision…… Do I dremel a slot for a straight screw driver, or do I drill a hole and use an easy out extractor? I’m calling it quits for today and will check back later for your screw removal suggestions.

imgur.com/a/2SkIdbu
 

Think i need a cuppa tea & a lie down after all that.
Ok, i'd get it out guaranteed, by peening the screw in a bit then get a "new" impact tip & drive it straight in "not with the impact tool".
Not sure if #2 or#3 but 5mm screws would be #2 i'm guessing.
Then when fully seated, fit the impact tool onto the bit without removing it from the screw.
Then--with the tool clicked in the correct direction--

That sounds like a great first approach because my ideas can follow if needed. But I totally understand your directions and I think it will work.
What scares me the most is that I totally understand your directions. lol