The two majpr problems are: the platforms can only take 8 cars; in the peak the line is close to capacity, so stopping peak hour trains on the Fasts has been a no-no as long as I can remember.
(@brad465 yes, there were offpeak TL services when LBG reopened - I went through to Finsbury Park that way)
IMO increasing the number of main line stops at Norwood Junction would be more feasible, though still not easy. ATM it's only 2ph in the peak, and off-peak the additional Coulsdon trains run immediately before/after the Gatwicks.