My first headphone tube amp was a Little Dot Mk2, it could only do 1 Watt into 32 Ohms. My only cans then were AKG 712, 60 Ohms and 105 sensitivity but that tiny amp had no problem driving them to ear bleeding level. Coming from a speaker setup will make headphone amps appear underpowered but you gotta remember that it only has to push air a very small distance. If you’re really worried, take a look at the Hifiman headphone adapter. It allows you to take speaker cables from a power or integrated into the magic box and output to a headphone. The Edition XS really won’t need this though.
Nearly all headamps feature a gain switch that can be set to low or high and will boost the signal before volume is applied. This is done to accommodate most headphones as they come in a much greater range of resistances than the 4-8 Ohms usually associated with speakers.
I love my TA30 for my planars but it sounds like it’s little higher than your budget. Not sure if it will work with your tubes either but it’s a strong 3w of power and has an Integrated dac.