Okay, you’re right to look at hybrid tube amps, as your headphones are relatively low impedance and in this budget range, you’re not going to get OTL that will play well with them. That seems to be mostly what you’re looking at, so all good.
I personally don’t advocate for budget dac/amp all-in-one tube units, though I’m sure people are enjoying them.
The MT-604 has its quirks, both it and the Loxjie P20 have no preouts. The MT-604 is balanced-only on its inputs, and you’ll need to convert from 4.4 to XLR I believe from your dac (or amp). That is doable. Obviously it has the separate left/right volumes and is balanced-only XLR on output, which presents challenge with your current roster.
MT-602, pretty good unit, pretty affordable, it’s single-ended architechture that should jive with your current cans well. Decent power, should be close to the single-ended output of your ZenCan. All for around $100, it’s a win. Schiit Vali 2+ also worth a look if reasonably available to you.