I think both protocols mentioned (MIP* = RE and the pointers one) already do what you want here. In the background the provers have to do unbounded work to prepare for the stuff they show the verifier, but the verifier’s work is limited to a fixed polynomial in the input size.
And more strongly: in the pointer version where we have two competing provers, a malicious prover can’t force an honest prover to do significantly more work than would be required in an honest case.
I think both protocols mentioned (MIP* = RE and the pointers one) already do what you want here. In the background the provers have to do unbounded work to prepare for the stuff they show the verifier, but the verifier’s work is limited to a fixed polynomial in the input size.
And more strongly: in the pointer version where we have two competing provers, a malicious prover can’t force an honest prover to do significantly more work than would be required in an honest case.