What if we could use the power as many times as we want, but suffer an accumulative penalty of -1 to all ability checks afterwards, like an exhaustion from an intense brain activity? Only the full long rest would then remove 1 level of this exhaustion. I think the penalty is just, considered the difficulty for an illithid check is 0. Maybe this could be solidified with a raise in a camp supplies count needed for a full rest - like from 40 to 100. That way we couldn't spam full long rests consistently.
