Keep in mind that, almost 10 years ago, EMF purchased KLRQ 96.1 Clinton, MO. Its transmitter is roughly 80 miles from downtown Kansas City. KLRQ never made any effort to target Kansas City before, and, when I lived in KC a few years before EMF bought it, KLRQ was regularly stomped on by the former KEFM from Omaha. However, they marketed it as "96.1 K-Love, KLRQ Clinton/Kansas City." EMF has since purchased a full-market signal for KC, and they refer it it as "96.1/97.3 K-Love."
So, judging from EMF's past actions, there's little chance they'll move 103.7 to Beaumont and the Triangle. I suppose it's possible they might market it to Beaumont a little bit, but they'll focus most of their efforts on Houston.