Reversible AND universal elementary cellular automata

Questions
1

Has any of the reversible extensions of the elementary one-dimensional cellular automata in NKS (e.g. Rule 37R) been shown to be computationally universal (like Rule 110)? If so, please give me links. Otherwise, could this be the case? Or is there a proof that no nR can be universal?

2

Wolfram mentions Rule 37R as an example of “cellular automata with class 4 overall behavior” (NKS, Chapter 11). “I strongly suspect that all class 4 rules, like rule 110, will turn out to be universal,” he says.