Are my cabling and bonding plans correct for a new subpanel?
Go for it -- just don't starve new the panel for slots!

You have plenty of headroom on your existing service to add the new feeder (the 220.82 calculation for your existing house comes out to a mere 45A, assuming your kitchen receptacles are on 2 circuits and your A/C is reasonably modern/efficient as I used a representative 13 SEER for calculation purposes), and a 60A feeder is more than enough for your guest suite, as NEC 220.82 pegs it at a mere 29A (given that it doesn't have its own laundry facilities -- even if it did, it'd be only 35A).

The wire's fine, too.  Even though 6/3 NM is only rated for 55A, you can't get 55A breakers, so the 60A breaker is fine as per 240.4(B), and the Article 230 provisions for service sizing don't apply to feeders.

One suggestion I will make here, though, is not to starve the new subpanel for slots -- something like a Siemens P3040L1125CU would be ideal here, even if it seems like massive overkill at first.  That way, there's ample space to arrange your load across circuits how you see fit.  Pulling the tie bar on the new subpanel here is precisely the correct move, as well -- neutral and ground never meet again, after all.