Try a search. Use "200S cab build" and see what happens; that should provide you with all kinds of reference info while you are waiting for a specific response to your "blapping" issue.
Truthfully it would be hard to go wrong if the internal dimensions are correct to the original. I've never built a 200S cab from scratch, but have used about every commonly used 15" driver (and some less common ones too) in 200S cabs and find them very forgiving of which driver you load in there. The only issues I've had is the magnet structure of some newer ceramics being too big to clear the port ducting.
Off the top of my head I would suspect an air leak, particularly if you built a rear loading enclosure true to the original and the problem occurs at about the same SPL with different drivers.
The backs can be a little finicky; sometimes they can hang up in a spot or two and not seal, and sometimes the back can distort a little if the torque isn't fairly even among all 38 screws.
You did use all 38 screws, right?
I make sure the backs aren't warped, fit flush, and drop right in without needing any hand or mallet "help", and then cross tighten the back mounting screws like lug nuts on a car.
Don't neglect to check the seal at the speaker gasket as well; over tightening can distort the frame and also cause leakage. Factory Sunns only use 4 driver mounting bolts, and the drivers are tightened "snug", not "cranked down" for this reason.
Good Luck, and welcome to the forum!