Would John Cramer's transactional interpretation require more complexity (at the level of the fundamental laws, rather than the amount of stuff in the universe) than the many worlds interpretation?

Neither the many-worlds interpretation, nor any retrocausal interpretation, has a canonical, ontologically satisfactory, self-contained definition as a theory. In both cases, you will find people who say that the interpretation is just a way of thinking about quantum mechanics, so the calculational procedure is exactly the same as Copenhagen.

If you dig a little deeper, you can find quantum formalisms which are self-contained algorithmically, and which possess some resemblance to the spirit of the interpretations, such as consistent histories (for many worlds) and two-state-vector formalism (for single-world retrocausality). I can't say that one of these is clearly simpler than the other.

By the way, Eliezer's original argument for simplicity of MWI has the following flaw. The comparison is between Everett and Collapse, and we are told Collapse has two axiomatic forms of dynamics - unitary evolution and collapse - where Everett just has one - unitary evolution. But then we learn that we don't know how to derive the Born rule from unitary evolution alone. So to actually use the "theory", you have to bring back collapse anyway, as a separate part of your calculational algorithm!

Roughly what proportion of the physics community backs it?

Retrocausality is a minority preference compared to many worlds, there's no doubt about that. It could be like 1% versus 20%. If you also counted people who are just interested by it, you should add a few more percent.

Is it ... [various technicalities] ?

It is meant to be relativistically local and that takes care of the majority of those questions. Whether it is non-differentiable or non-deterministic would depend on the details of a proper retrocausal theory. For example, Wheeler-Feynman theory is just classical electrodynamics with waves that converge on a point as well as waves that spread from a point, whereas the two-state-vector formalism is stochastic.