I would just like to make a suggestion: if you don't really know what a DAC/Amp are doing for your headphones then I think it's probably a mistake to jump right in with a $1300 spend with the idea that you'll suddenly have this magic setup. The key realisation about hifi audio for me is that it's most definitely a subjective journey. What you want to do is figure out what sort of sound you like. Do you dig the bass, or do you love the feeling of clarity that comes with great treble? Are you into vocals, do you like fun music, or do you like utterly re vealing? I think if you spend right out of the gate you need to be prepared for the idea that you're going to probably change your mind about what you like in the future, so you'll end up spending more in a relatively short period of time.
I started out with an aune x1s ($250) DAC/Amp combo and a pair of Beyer T90s ($300) - it's very neutral, a little bright, but introduces you to clarity and some wider soundstage. If you swap out the T90s for the Meze Neo's I think you'd also have something really worth listening too.
For there you've got $450-750 to take your next step. If you're liking that current sound of your headphones then you'll want to work on your amp setup, or progress down the neutral headphone route into the expensive stuff (Aune X1S -> Hugo2 for example, or T90s to T1m2, or across to Senn for the 800S). But you can also switch up and try something more warm or bass heavy, something more fun. There's so many headphones to try, and there's the whole dac/amp world to explore. I love my Elears and TH-X00PH, and getting into tube amps has made for some wonderful experiences. Now I switch headphones around depending on what sort of music I listen too and it makes the hobby more fun
I've got a Mojo, for example, and I think it's better than the Aune, but it's a PITA to have on my desk all day (small and wobbles about, requires charging, gets hot, volume buttons annoying, some format problems) and since I got a decent DAP it's just something I don't use much anymore - because it's really not great portable from a phone as a source, cables wobbling, charge issues, heat etc. It was a bad buy for me - I should have spent time with some cheaper stuff, then bounced straight to just using a chord DAC for a better Amp.
That said, if I had to maximise $1300 for utter enjoyment then i think the best combo of the gear I have would be trying to land some b-stock Campfire Andromedas and put them through a Sony zx300a (you need to order from China). Should come in right on the money, if you're lucky with the b-stock or second hand, and the sound is amazing from that combo. The Andros are IEMs but I find it hard to say enough good about them for their price. And the ZX300A (without the A it's much more expensive) is a steal for the money.
I guess the tl;dr is: don't spend the money all at once because you'll probably change your mind, or at least want to explore, as you grow into the hobby