Sell everything and get an Atari ST, you'll never have a dilemma there let alone a trilemma
On a more serious note and subjectively judging by what you mention, you should go the 060 way.
You obviously care enough about those AGA+060 later demos to reference them.
With a 060 you definitely won't stick to a floppy-only system, so I expect you'd use WHDLOAD for your gaming, where things mostly work with the 060, might need some option fiddling here and there at times but generally that's about it.
Still, for the occasional no-go, you can disable the 1260 altogether at boot-up by pressing the non-numpad "2" key and floppy-boot the misbehaving game natively.
The lack of a full FPU on the 060 is vastly a "non-issue". I'm not a demoscene expert but I'd think few if any FPU-oriented demos would rely specifically on the 68881/2.
The only nuisance is you need to properly install the 060 libs beforehand.
And maybe some extra heat produced, though a fully-fledged 1230 + FPU @ 50 Mhz isn't exactly ice-cold either. But that's addressable, too.
PS verify your A1200 is in top-shape (caps) and the PSU is adequate (e.g. the older A500 PSU with 4.5A on the +5V line is enough for a 1260). The 1260 doesn't generally require any timing fixes on the A1200 motherboard regardless of revision so instabilities are usually capacitors/PSU related.