I haven't been able to find a statement relating $\mathsf{MA}$ and $\mathsf{NP}^\mathsf{RP}$ in the literature; pointers would be appreciated.
I believe they are equal:
$\mathsf{MA} \subseteq \mathsf{NP}^\mathsf{RP}$: The $\mathsf{NP}$ machine guesses Merlin's string, and the $\mathsf{RP}$ oracle verifies the string as Arthur would.
$\mathsf{NP}^\mathsf{RP} \subseteq \mathsf{MA}$: Merlin guesses the accepting computation of the $\mathsf{NP}$ machine, including all calls, as well as the outcomes of these calls, to the $\mathsf{RP}$ oracle. Arthur then verifies that the computation is valid and that all the guessed outcomes of calls to the $\mathsf{RP}$ oracle were correct. He uses amplification and union bounds to bound the overall total probability of error.
Is this correct?