I read, somewhere on the net, about burning compacted sawdust by having a central hole,don't see any reason why, if it works, it wouldn't also work for cat litter.
Presuming the stove has a bottom grate to feed air,you could try getting a 2inch stick ( it might help when extracting it to wrap it in paper ) hold it upright and pack the litter firmly down. Remove stick then rip up the paper, drop the pieces down the hole and light, preferably from underneath.
The idea seems to be that the hole forms a sort of chimney and the litter/sawdust burns from the inner circle outwards due to the forced draft.