Many tyres are handmade, and as such could well have wobbles. Apologies if this is all old news to you but:
Check you’re putting your tubes in when inflated enough to hold their shape [not inflated/stretched, just torus-shaped], twists and creases will cause wobbles.
Smear soap around the rim hooks/tyre before putting them on.
Seating tyres by putting 2-5psi in them and spinning them in your hand looking to check the same amount of bead/seam shows all around before pumping them up.
Sorry to contradict you here Jim, but I really wouldn’t be putting 60psi in a tyre until you have FIRST checked the seating. Yes it will settle, but if it’s hanging off somewhere there’s going to be a monumental BANG, especially if you’re inside!