The answer to the OP (opinions, valid or otherwise aside) is no, you do not have to have a certificate of release to service on any part on a permit aircraft and no Part 145 has no bearing on permit aircraft, or their engines. You can in fact do it entirely yourself so long as you have an appropriately qualified LAA Inspector willing to sign off the work.
The answer to the question, "should you" use a part 145 company to rebuild your engine is wholly subjective. I know I would find a person who has a reputation for quality and reliability and they may or may not have a Part145 authorisation - chances are they do but given it's the engine of my aircraft
I'll go with the safest rather than the cheapest option
Do whatever you think is safest