Well, then you'd need to define an arbitrary time limit for how long it would take to form a sphere. In which case, you might as well have just defined a size/mass limit in the first place.
I think the definition would be that they're presently a sphere, that was formed under its gravity. That way objects could possibly become moons in the future, but the timescales are so long it's mostly irrelevant
That's technically correct (the best kind of correct!), but I think it's a misleading thing to state. The reason all objects eventually become spherical is because they eventually disintegrate into the nearest significant source of gravity, which will itself be a sphere. It's not as if, hypothetically speaking, an immortal human being floating through space without orbit would eventually morph into a sphere under the pressure of its own gravity. Rather any object is naturally going to decompose into parts which will be spherical or adjoined with an already spherical object.
Even if the conjecture that sufficiently high entropy causes quantum physical effects to dominate macro-physical spacetime is correct, long before that happens there won't be any objects left which aren't already spherical.
Actually, not always. A mass orbiting close enough to a planet is subject to tidal forces that will rip apart and eventually flatten a round body into a ring.
If body is in a strange orbit taking it in and out of the roche limit, it will adopt some strange middle ground between bring a round moon and a flat ring. Inside the limit, material will be ripped away from the body and flattened towards a ring. Outside the limit, that material will fall back nearer to the equator. So you get something like a ball with a belt.