A thorough check on several rulings seems that indeed this combo is Legal, although quite hard to actually pull or be realistic to play.

I had my doubts with the monster trap, as they are both trap and monster (except Paleozoic cards), but found a ruling that states that if imperial custom is up then the trap monster is indestructible:

If “Embodiment of Apophis” is being treated as a monster while “Imperial Custom” is active, it cannot be destroyed by effects or battle.

Now, as others mention, this combo is not a flawless lock; your trap monsters are still exposed.

You can get rid of those trap monsters by banishing them, sending them to GY, returning to hand/deck, flip face-down (which sets the card as Trap again), change control, tributing them, attach as XYZ material (with Number 101: Silent Honor ARK for example), or negate their effects (which returns them to the Trap zone, negated).

A thorough check on several rulings seems that indeed this combo is Legal, although quite hard to actually pull or be realistic to play.

I had my doubts with the monster trap, as they are both trap and monster (except Paleozoic cards), but found a ruling that states that if imperial custom is up then the trap monster is indestructible:

If “Embodiment of Apophis” is being treated as a monster while “Imperial Custom” is active, it cannot be destroyed by effects or battle.

Now, as others mention, this combo is not a flawless lock; your trap monsters are still exposed.

You can get rid of those trap monsters by banishing them, sending them to GY, returning to hand/deck, flip face-down (which sets the card as Trap again, as explained here), change control with other monster, tributing them, attach as XYZ material (with Number 101: Silent Honor ARK for example), or negate their effects (which returns them to the Trap zone, negated).