Would a wheelset cost you something in the range of what a decent used entry-level mtb would?

What about cyclocross tires, which come in a 700c?

What kind of gravel are we talking? Really fine like what you'd find on some rails to trails or more coarse?

Yes, if you ride at max air pressure less would help. Not too much less or it'll be squirrelly in a whole 'nother manner.