This is where the military "deadside join" (not an overhead join) has an advantage. It was designed for a busy circuit. The joining aircraft avoids the liveside pattern, by flying parallel to the duty runway, on the deadside at circuit height and fits into the pattern on the crosswind end. If anyone has to extend, it's the joining aircraft and he goes further upwind. This avoids anyone having to fly the dreaded "extended down wind leg", which gets longer and longer as more aircraft have to follow suit.
All of this can be done equally, or even better, from a standard overhead join. I don't understand all this fuss, neither do I see any advantage to a deadside join vs. an overhead - overhead join is published standard, 500 feet above circuit, though it can of course be overridden by local practice but then this should be published. And how are you going to check the signal square from a deadside join?
The only reasons for NOT joining overhead are glider winching and parajumping - both should be covered by adequate published procedures. Or am I being naive?