I’ve been daily driving a dedicated DAC+AMP setup on my PC (Schiit stack, HD600) for a few years now and I have to say, the difference, if present, is minimal at best. Unless the DAC in the Deck genuinely measures poorly, (which I don’t believe it does), a new one is unlikely to be better.

Also, external DACs in general are almost placebo-tier hardware. I highly doubt that you (or many other people, for that matter) would be able to tell the difference between the two in a controlled ABX blind test. Even if you could, the conditions you’d need to pass such a test (laser-focus on the audio, quiet room, high quality audio that you are highly familiar with, etc) would not be present while you’re gaming on the Deck.

If your pair of Sennheisers really is good like you say it is (and the Deck can power it at acceptable volume levels), you don’t need to waste your money on any other gear.