Your questions:
Can I cut down a cam (compression release) safely on a lathe?
Yes, and you can remove that bump with an angle grinder. You won't feel a heck of a lot of power increase. If any. Look in to getting your cam modified by Tim Isky. (310)769-6880 Or, you can maybe find one of the Dyno OHH 245's around.
Bung the cover until I can find a replacement?
OldMiniBikes Member Rick Chatten posted the information
here, and cites it as a 7/8 freeze plug. I see no reason to cut off a PTO cam shaft. It doesn't even show once you have the clutch mounted. There are probably members right now who have HS cams and covers just taking up space by the way. If you want to change them, put out a wanted ad.
Invest in a billet rod and new piston and rings? Remove governor?
The rod is the ARC 6282 Billet Rod for the 5.5 OHH engines. Replacement rod is the best engine survival investment you can make. It is the achilles heel of a Tecumseh.
I've never replaced the piston, but I do check the skirts against the manual.
I get the rings from Ebay usually. Don't bother ordering any until you've measured and corrected your bore. I like to shoot for the minimum end gap.
Yes, you can remove the governor once you get that new rod in. I tap for 10-32, and drive a machine screw in with Loc Tite 620. (green) Remove the spool from the block as well, but you can leave the shaft.
Valves and springs?
For stock RPM ranges, stock valve train is fine. Delray did some work and found that the components below work just fine, although the spring retainers needs to be modified to fit the spring. I used my drill press as a lathe, since I don't own a lathe. Not a problem.
Dyno AN-001 18 LB valve springs for the Briggs Animal.
Briggs DCSH103 valve keepers for the Flathead.
Briggs DCSH102 lower valve spring retainers for the Flathead.
If you do all of that work, you're going to want to ditch that Tecumseh carburetor. You generally have to make your own intake manifold. I've seen some folks use the original with some cobbled up adapter on the end, but that just impedes flow, and looks ugly. There have been some manifolds cast that will fit a Mikuni to an HS. At that point, you will need to incorporate a vacuum nipple from that manifold (best) to power the fuel pump you need because the OEM manifold and carb sits low enough for gravity feed.
I built one of those engines for a project, but didn't document it much, since others were doing the same thing.
This test video is the first time I started the engine, and I changed jets and experimented with the metering needle. Carb is Chinese Mikuni, VM22.
Those of us who built these engines used bearing PTO cranks and side covers. They are superior in handling loads over the "recreational" bushing engines. Delray actually machined the crank and block for the mag side as well, resulting in a superior rotating assembly. But you can get by with a bushing engine. Just like you can get by with a totally stock engine. It is also possible to machine a crank to accept a bearing and fit a bearing side cover.
Look up Delray's work on that, or he can chime in.
@delray Also,
@OND might have some interesting solutions on powering lil Indians.