I've never been in a situation where I couldn't allow Apoxie the full 24 hours so I can't help you there... but they do say it can be painted before it's cured so I guess it's safe.
I handpaint my FBRs, too, and I usually give it half an hour to an hour between coats. In practice it's often more but that's only because I start doing something else in the meanwhile and then forget to get back to painting.
With smaller areas like eyes and symbols I usually just wait until it looks and feels dry enough to add the next coat. Then again, I do a lot of wet on wet painting, too.
I assume with an airbrush the drying time between coats is not as critical, the reason you have to wait with traditional paintbrushes is that the bristles may lift off paint if the previous coats are still wet. However, if possible, I would give the pony one or two days before sealing and rehairing to make sure the paint is fully dry. If you're quick with rehairing, I'm sure you'll be able to finish by Monday.