Unfortunately, there are two options - use a third party’s Secondary DNS or run your own, on a different VPS.
It is not really difficult to set up a name server that can be used as a secondary. BIND is the gold standard in some ways, but PowerDNS is actually easier to set up for use with MiaB.
You could get a $2/mo VPS with 512mb ram from BuyVM and handle this easily (with BIND) if you really do not want to use a third party and wish to be economical.