How much time are you thinking it should take to DTP? It doesn't seem like that much of a time savings to do pullups vs deads or PC. Particularly if you do 3 sets of pullups or dips? For instance on deadlift day, I do 3-4 warm up sets of 1-5 reps with very little rest. Then I rest a bit and do the one set of 5 and thats it. Maybe you're taking too long on your warm up sets?