I can't comment on how much DACs influence the HE6se V2 as I only have my one, the Schiit Modius. I think it mostly depends on the amp in your chain. Some amps might not have enough headroom to EQ to headphone if they're only getting a 2V signal from a non-balanced DAC. Similarly, some hybrid amps are Class A through most of their volume range and switch to Class A/B at the top end, and a 4V signal might provide the headroom to keep the amp in its pure Class A range, whereas a non-balanced 2V signal might require pushing the amp into a volume range that means it switching to Class A/B and thus degrading the quality.

So, it's hard to say how important the DAC is without knowing what amp it's being connected to. But the Schiit Modius like I have is a good 4V balanced DAC that can be had for just $200, so again you don't really need to break the bank. You just need to know what to buy.

I don't have any experience with specifically 2-3W amps, my amp collection jumps from 1W to 4W. So maybe there's a 2-3W amp that would make the HE6 shine, but the general consensus from the Head-Fi HE6 community is that you need to start around 4W.

A thing I dislike is that this all can sound very gatekeeper-y and I hate gatekeeping in any hobby, so I am again eager to point out that, while this headphone does seem to benefit from every watt you can give it, you don't have to spend a lot of money to get all those watts. Good +100WPC speaker amps can be found used for around or under $100 very easily and they are a very popular and inexpensive way to get heaps of enjoyment out of this headphone. There's also the Emotiva BasX A2m that's normally $350, currently on sale for $250.

You don't need to spend a lot of money to get the best out of this headphone, you just need to get exactly the right gear.