Let's say (for argument's sake) that the Alien Queen can not lay a
fully developed egg without the egg sac. Alright?
Perhaps she can still begin the process of an egg (Phase 1), kinda like the life process of an Alien:
Phase 1 - Embryo
Phase 2 - Chestburster
Phase 3 - Skin molting phase
Phase 4 - Adult/Full scale
The Royal facehugger can carry it very easily without fear of damaging itself, therefore can climb to extremely unlikely places to avoid being checked for. The egg can adapt to it's surroundings and the life cycle continues. Meanwhile, the Royal Facehugger can scout for victims for itself and the soon to be hatched facehugger. Once ready, both go on their final mission and impregnate the victims with their embryos.
A tad far fetched, but still believable. Right?