Sorry for the delayed response. I've been out of town.
I would assume that this is a square-tapered spindle from 1986. Sounds like you might get away with replacing just the bottom bracket. These came in English, French, and Italian threading, so you need to match the cups with the frame dimensions and threading. Italian has right hand threads on both sides, English has left threads on the left side. Miyata is Japanese and I think they used English spec bottom brackets. Spindles also come in different lengths for double or triple and sometimes smaller increments to improve the chain line. Did you inspect the bottom bracket when you had it apart? Is there pitting or scoring on the bearing faces? Are the cups worn excessively? Are the outer flats where the crank attaches still flat and smooth?
If you simply told me that the crank had play, the most likely reason would be that the crank-spindle interface was damaged because somebody rode the bike without tightening the crank arms on properly. If the whole bottom bracket is moving, then that's not the (only) cause. Either this bottom bracket is badly worn or parts of it are simply the wrong size (and probably very damaged because of that). I'd suggest replacing the entire bottom bracket. You might end up with a sealed cartridge bottom bracket just because they are easier to find these days. If the flats of the old spindle and the cranks show no damage, you'll probably be fine with fitting the old cranks on the new spindle, but you'll have to try to be sure. If that doesn't work and you end up needing a new crank anyway, then you won't be restricted to square taper bottom brackets, but you'd want a crankset that matches a 6-8 speed cassette because chain widths and chainring spacing has changed over the years.
Oil is good, grease is better.
2007 Peter Mooney w/S&S couplers/Terry Butterfly
1993 Bridgestone MB-3/Avocet O2 Air 40W
1980 Columbus Frame with 1970 Campy parts
1954 Raleigh 3-speed/Brooks B72