If you really want to increase your TT get your CFI/II/MEI via the military conversion with the FAA. Fly on the side as a CFI if there's a local airport.
The airlines have made exceptions for some people. Typically senior officers in non-flying jobs. Talked with an O-6, on the O-7 track, who rarely flies and won't have 100 hrs/year. Why? Because his value to the USAF is as a senior officer. The airlines, or at least some of them, understand that.