I would just place plexi glass for the first 6 inches or so of the bottom of the doors. This should prevent the crickets from climbing up the walls.
ALso you could feed the crickets in a dish high enough to keep the crickets from easily climbing out (though tehy probably will just jump out) and low enough for you bearded dragon to step into it. I use a cheap ashtray I bought at the local dollar store to feed my bearded dragon. I can't remember how old your dragon is but if he is young enough that the crickets perfect for him are half an inch or smaller..shouldn't be any trouble for him to eat them before the crickets have a chance to climb out. What I do is place the crickets in a small sandwich bag and pour them into the ashtray a little at a time..giving my beardie time to gobble up all the crickets....less chance of the crickets running hiding before being eaten. Also an easy way to track how many he eats. Easy to dust crickets too, as you just add the multivitamines and calcium powder into the bag, shake to mix, toss in crickets and shake again to coat them.
Hope this helps.