So my best guess after seeing the mag.... A bad crank seal is very possible. The points are EZ enuf to replace but are behind that flywheel. So...
1. Outer case off
2. Soak down flywheel center thoroughly with a substance like PB Blaster if you have that there.
3. You will need a center pull flywheel puller that threads into those big dia threads after your remove the flywheel nut.DO NOT TRY TO USE AN EXTERNAL PULLER..... USE THE RIGHT ONE!
4. The flywheel is probably really on there. Put pressure on the puller by holding with one wrench and torquing with another. It may help to put a turn or 2 on the puller then let it sit for a while to get penetrating fluid into the taper. Some guys tap on them. I don't like to do this as it may damage the crank end or puller threads. After it sits a bit then try again and usually off comes the flywheel.
5. Let me say I don't trust your re-build guy. Nothing was cleaned up in there. There should be a keyed, tapered shaft that you need to clean off, but first look right at that rubber seal around the crank! Bet that drool trail can be traced right to it. That seal was likely NOT REPLACED.
6. Replace the crank seal. I think you should be able to use a small lady finger like pick to get it out. A seal shop can get you another from the numbers on it. At this point have someone hold the bike down firmly (a fat friend helps here), and see if that crank play is evident. should be no up/down at all.
7. Your condenser is right with the points plate. It is an alum cylinder about 1/2 in by 1 1/2 in long with 1 wire off from it. If you can get points or if yours look bad.....well now is the time to replace those 2.
8. Crankseals must be put on proper direction and I usually use a little Vaseline to put them over that cleaned shaft. Carefully and uniformly press back into the case. Key back in shaft and lightly tap to seat it. Points and cond in? All wire nuts tight? Time to put flywheel carefully back on. It should go most of the way back on and feel snug BEFORE you try to tighten the nut. Torque to spec. Usually hardest part is devising a way to hold the twisting flywheel here. There is a proper clamping tool to use and you might borrow one. It goes around the outside of the flywheel dia and lodges up against the case to hold it still.
Yup, some more work to do................