Not applying pressure while shifting is wrong too, IMO. To shift properly you need a certain amount of pressure. Not too much, not too little. The cautions we've made for ages about not pedaling hard when shifting seem to have gotten rewritten over the many years to "be delicate with pedaling when you shift". Which isn't correct. You can actually pedal fairly normal if you are not grinding out a climb at 30 rpm trying to get out of cogs you should have shifted out of well before that time.
However, for the issue the OP has, I'd investigate hanger alignment or check that the DR isn't bent itself. This is the existing DR wasn't it?
What happened to make you replace the hanger?.