I am definitely up for a little more automation - we have established a routine of explore the room -> search for traps of chosen next door -> enter next door, repeat the cycle.
For example with the last post, the only thing Lith could do is pick up his dart and go to his position in the marching order, waiting for the GM to describe the next room (since we are searching the door, I would expect we are entering it). Could we, in the case where no traps are found, be transported directly into the next room?
If the filler rooms have only one exit, I would prefer them to be mentioned in passing and be transported onward.