Where do you get the assumption that those filing to run don't live in the district? Isn't that a requirement to run for the House?
No. The Constitution only requires that a prospective House member be an "Inhabitant of" the state he represents "when elected". He or she need not live in the district he or she represents. In theory, he or she doesn't even need to live in the state until election day.
In fact, there are a number of current Representatives who don't live in their district (some of which have shifted due to redistricting). I think Florida has several.