DAP has its advantages like separate battery with extra life. If you don't need this having a card full of music loaded onto your phone that's connected to a DAC could give you an upgrade you're looking for.
This is possible but seeing the OP already has a DAP which includes a very respectable DAC chip I fail to see it is of any benefit unless you are suggesting he sells it on.
As an avid DAP user whilst away at work I consider DAPs superior because of storage rather than battery life, although this is a fact. My DAP has two dac chips and, as far as I am aware, isn't going to be bettered by an external DAC whose extra cost would seem to defeat the object of having an all in one device.
For me the only way onwards and upwards is to upgrade my iem which I have done with great success more than once.
Upgrading to the Norma is quite expensive and I am not too sure the sound quality would be hugely different to what he currently has. I'd suggest only an audition will resolve this question.
I am a great believer, having heard many DACs, that expense does not necessarily bring improvement, certainly in a bangs for bucks scenario, what it does bring is a different presentation of your music. Whether you deem that new presentation as better is very much down to the individual.