Oh yeah! Got it all fixed today! I'm not sure exactly what cured my chainline because I did a bunch to it all at one time.
First thing I did was bought a new freewheel. Just another Shimano one, same size. Pretty much hoping that it was dead-on straight.
Second, I bought these:

Not exactly the color I wanted but they don't look half bad. The work really well and very adjustable.
So I took it for a test ride, and was so happy I put some Ultegra dual pivot brakes on it in celebration. Also found some nice pedals for $30, and some metal toe straps. I feel like I just got a new bike... and good thing because I dropped about $175 on it after some discounts.