Well I loaded up the model and don't really know what to suggest short of just going in and manually fixing all the tri's.

There is no AUTOMATIC way to correct this without adding tons of useless geometry into your model.

You could make the mesh active and build a new CLEANER mesh on top of it.

It's best to try to keep the topology clean AS you are building rather then allow so much chaos to build up then try to fix it at the end.