Torque converter: to shim or not to shim?

I believe that will be fine, I haven't read of what the clearance space should be. The actual worst case is if there is no clearance, which is somewhat common to read about when an engine fails, due to an eaten main thrust bearing. The torque convertor has to engage the trans properly, that's all about going in all the way to engage all spines and the pump fully. If the TC doesn't slide back and forth once the engine and trans are together, that's when you stop and re-seat the TC properly.

But the proper clearance there I'd bet is in the 1/8"(low side) to 1/4" range. As I said I hadn't heard the official specs for that. Is it the same for all Ford automatics, I'd expect it's very close for them. I'll let you know next year about a 6R80 behind a 302 block.

“Somewhat common” Should be change to “pretty-much guaranteed”...... lol

Yes there are nicer washers than typical hardware stuff. The SS take some time to find, the McCarr and Fastenal websites should have tons of choices. Some Fastenal places no longer carry the full catalog of parts though, many sources are going away.

The fact you have some play is very good. Using OEM convertors requires less double checking. It is wise to check any combination of non stock parts for a TC etc, that end play is really important. I'm planning to measure that when I pull my 302/4R70W out, right when I take the nuts off of the convertor and the bell housing bolts are still tight. That's the measurement you want to aim for when putting it back together.