So we at least had a level of trust since they'd cleaned their house for so many years....
It worked out great having cleaning every other week, but weekly probably would have been even better and prevented them from slacking. It turned into a situation where I think we'd do such a thorough job cleaning up after ourselves on the off week, that when they came in to clean on the scheduled week, there just didn't appear to be much for them to really do....

Ultimately though....wife and I just determined that our standards of clean are just several levels above what our neighbors consider to be clean....