Kit's idea has some merit and makes a lot of sense. And there would be a couple of different options here:

Basehor, obviously, has a big enough gym for four mats, as does a facility like Saint Mary College in Leavenworth, and those could be viable options.

The other alternative would be assigning the meet to two sites at a time (have seen this done before for volleyball). It would go something like this:

Lansing and Immaculata host with the finals at Lansing, or
Mill Valley and Bonner Springs host with the finals at Mill Valley, or
DeSoto and SFT host with the finals at SFT, or
Piper and Basehor host with the finals at Piper, or
Tongie and Perry host with the finals at Perry.

Of course, if the KVL ends up being an 8-teamer like it sounds it could be, this is all moot, too!