Simple: Instead of being able to warp to just depths 0, 8 and 18, let knights choose to begin at depths 4, 13 and 23.
Warping to depths 4, 13 and 24 would cost 100, 200 and 500 crowns (particular prices open for debate), but you must first have reached the depth of that particular gate, similar to how you unlock free warps for depths 0, 8 and 18.
Basil will not have anything in stock if you warp directly to his depth, but you will be allowed to access shadow lairs.
No matter what, warping costs crowns? I'm good with that idea