Recent work with laser-cooled molecules in attractive optical traps has shown that the differential AC Stark shifts arising from the trap light itself can become problematic, limiting collisional shielding efficiencies, rotational coherence times, and laser-cooling temperatures. In this work, we explore trapping and laser-cooling of CaF molecules in a ring-shaped repulsive optical trap. The observed dependences of loss rates on temperature and barrier height show characteristic behavior of repulsive traps and indicate strongly suppressed average AC Stark shifts. Within the trap, we find that $Lambda$-enhanced gray molasses cooling is effective, producing similar minimum temperatures as those obtained in free space. By combining in-trap laser cooling with dynamical reshaping of the trap, we also present a method that allows highly efficient and rapid transfer from molecular magneto-optical traps into conventional attractive optical traps, which has been an outstanding challenge for experiments to date. Notably, our method could allow nearly lossless transfer over millisecond timescales.