Well, I think I figured out what was wrong with the transmission. I removed the angled drain plug as Pabdt suggested. Some sludgy oil came out, but you know what didn't come out? The stopper cam or spring. That's right, someone went to change the oil in the past and lost them. Does anyone know where to get a good replacement? I'm not sure the bolt I have is the original either. It has a raised nub at the end rather than a recess, as this diagram seems to show: www.cmsnl.com/yamaha-dt250-1976-usa_mode.../partslist/C-07.html
I know some of the bikes used a spring and a ball bearing, is that a possibility on this bike or should I try to find the solid cam? Thanks for all of your support so far! This has been a wild journey. I am moving into an apartment that doesn't allow you to work on your own stuff, so the clock is ticking for how long I have until I need to have this bike finished.

The special cap nut thingy is hollow with a 14 hex spanner size. The plunger is hollow & Spring fits inside. It all slides in the nut part. Ball & Spring would have limited success & be a big ball to fit good in that hole. If you went that way as an easy fix until parts arrive just be sure there's no chance the ball can escape past the drum cam & enter the gearbox but I'd guess a big enough ball wouldn't get past there & enter. Best get the right thing!!. Common to loose those items & a trap for those that don't know. Cheers.

I feel a bit silly now... I was looking closer at the part that I removed from my bike and I realized that all of the parts were still together, it was just seized in the fully compressed position! I gave it a few little smacks and it all came apart, of course filled with rusty water. I think I should be able to clean it up and use it. The spring still seems to be in decent shape, I don't think it is too compressed. That makes things a bit easier! I ordered the proper gasket for the clutch cover, since the previous owner removed it and replaced it with cheap silicone. Hopefully it will run and ride normally now!

All good & there's great satisfaction in sorting it yourself.
I feel silly now haha, "if i'm on the right post", as i thought it was the change teeth engagement out by one tooth.
Hope she's good now after freeing it all up. Cheers.

It's been awhile since I last updated, I've been waiting for parts and I also adopted an '86 Honda Spree this week. I do have good news today! I received the gasket today and installed it, then took the bike on a test ride. She rode great! The engine still sounds pretty rough because of the bearings, but it really runs pretty well. It also shifted through all 5 gears no problem. That stopper cam was the issue for sure. I ended up ordering a cheap "universal" motorcycle seat off of Fleabay to install, I think it will do just fine.
On sort of a sad note, I think I will be done with this project soon. I am moving to an apartment that doesn't allow you to work on your own stuff, so I need to get the bike a new home. Out of curiosity, is there anyone near the Spokane area that would be interested in continuing this project? I want to find it a good home, in a perfect world I would see this through to the end. Either way, I'm just happy to have got it as far as I have! Big thanks to everyone on here that has helped me out, I really appreciate it.