"ATH-W1000x" is more clear than mysterious specs in your OP. Well, tubes are you way. ATs like current and you likely love (will love) tubes. Combine these and your options are:
- Either some horse-power amps Uncle Eric mentioned above.
- Or some affordable options, like hybrid or transformator coupled amps.
My friend likes his SOHA II > W5000 rig. Another one enjoys TTVJ Millett Portable with ATH-EW9. Both amps are hybrid. I tried both ATs mentioned above along with W1000, AD1000, AD1000PRM, AD2000. And I will prefer tubes any day with all these cans. Go tubes.