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What would probably be the best amps single-ended and balanced for under the aforementioned price?
A balanced beta22 would be good. Or a Zana Deux if you're into tubes.
The balanced audio-GD phoenix headphone amp is coming soon also for about $1000 I believe.
I will add the Woo Audio WA5 LE. It is pure audio bliss.
For a solid state single ended amp, be sure to consider the Luxman P1. TTVJ may not carry them now but they are available from Japan. Worth the wait. You can spend more to get less
This is musical amp that will get you're toes tappin.
What about the Zana Deux Transformer? It's balanced too.