Suppose I get in something that is billed as a transporter, but which does not preserve computational continuity. Suppose, for example, that it destructively scans my body, sends the information to the destination (a process which is not instantaneous, and during which no computation can take place), and reconstructs an identical body using that information out of local raw materials at my destination.

I don't know what "computation" or "computational continuity" means if it's considered to be separate from causal continuity, and I'm not sure other philosophers have any standard idea of this either. From the perspective of the Planck time, your brain is doing extremely slow 'computations' right now, it shall stand motionless a quintillion ticks and more before whatever arbitrary threshold you choose to call a neural firing. Or from a faster perspective, the 50 years of intervening time might as well be one clock tick. There can be no basic ontological distinction between fast and slow computation, and aside from that I have no idea what anyone in this thread could be talking about if it's distinct from causal continuity.