Other solution would be to make a multisig address where you and someone trusted operate the exchanges, but this won't provide instant liquidity as it requires you to sign manually afaik.
it can be automated like any other operation. it is just a matter of creating a public key and sharing it with the user so that you can both create a 2 of 2 multi signature address. but there are other problems with this design which is fraud like what if the user or the site refuses to sign the second part of the transaction after they received the payment?
saying that makes me think of Lightning Network and Atomic Swaps. if OP can implement THAT, then there would be interest in it. otherwise there already are trusted services that do exactly what he described in OP.