I think that beyond a certain period you have so much logic at your disposal that you can construct two organisms sending messages to each other and vary the distance in increments of one to get any period you want.
You're basically correct, though it's usually done with 4 mechanisms making an adjustable glider loop, which can have any period of 43 or more just by increasing the spacing: https://conwaylife.com/wiki/P43_Snark_loop