Show that there is an efficient zero knowledge proof for any language $L \in NP$
Your idea is correct. Although the running times of the honest prover and verifier do increase by the running time of $R$, this (somewhat counterintuitively) does not affect the concrete bounds for soundness and ZK (at least how they are usually defined).
Note that $T$-soundness does not really make sense for a proof system, since it is sound against even unbounded cheating provers. However, it does make sense for an argument system, and here we don’t really “lose” the reduction $R$’s runtime: any $T$-time cheating prover $P_2^*$ for some instance $x \notin L$ is itself a $T$-time cheating prover for the instance $R(x) \notin A$, because it fools the verifier $V$ (for language $A$) without doing any additional computation. The latter does not exist by assumption, so neither does the former.
Similar reasoning holds for ZK: a $T$-time cheating verifier $V_2^*$ for some instance $x\in L$ is itself a $T$-time cheating verifier for $R(x) \in A$, because it plays the role of $V$ in talking to $P$. So, we don’t need any additional computation to “gain knowledge” from an interaction with $P$ about $R(x)$.