Can running in stability shoes with right forefoot varus cause the right hip to rotate anteriorly (to bring down first ray b/c cannot pronate)?

No. The answer is no better to place no posting on the heel and place the forefoot in valgus.
It can but. You need to get evaluated. Your gait cycle should be evaluated barefoot and with your running shoe. Custom orthoses may be necessary. Stability shoes or over pronation lasts really do not help much because they are tailored for the general public. Your condition sounds highly specific so professional eval is more appropriate.