I'm not suggesting only using Skirmish maps, but applying that format's placement method with any map and making changes as necessary.

For example, a 16x24 map could utilize 2d8 for alpha and 1d20+1d4 for numeric to cover the whole map. Or you could divide the map into quadrants of 8x12, rolling 1d4 to determine the corner (1, 2, 3 or 4) and 1d8 + 1d12 to determine the square within.

Sounds fine but with slips, I don't end up with 2 characters in the same square. I still have to repick when they land on blocking though so there's no avoiding a certain amount of that no matter the method.

Or use a generator off of the tinterwebs.
Need to read up on skirmish.

The interesting thing about you v you is that it's fair.
The dice and the dials change the plans up and its cool to spot things you didn't initially see.
I have fun.