What is the source of the turn-on thumps? Is it the power amp or an upstream component feeding the power amp?

Most turn-on thumps are fairly low in frequency and brief in duration. I would not put a relay in the tweeter circuit. The crossover will attenuate the turn-on thump also.

If the unshilded drivers are OK with your RPTV, fine. I don't know if a compass is sensitive enough to use as an indicator in CRT applications. For conventional CRT tv applications, shielded drivers ARE needed.
If shielded versions of the drives you are interested in are available, I would use them so that the center channel speaker can be used with other TVs

Paul