I think this may be too many constraints. I have tried making a 20 round schedule, going 7 times to 1 court, but I can't do this without avoiding some people playing 3 games in a row, and also losing the 'against everyone twice' property. Therefore the best solution to the problem as stated, is probably to modify the 11 rounds 3 court schedule to become a 22 round schedule, where each round of the former is converted into one round on two courts followed by one round on a single court, this would make sure that nobody plays more than twice in a row.
Ian.