I have auditioned all 3 of your top list and bought the HP4. It is by far the most flexible with high Z and low Z inputs and single ended and balanced outs and much much more. Its a fantastic heirloom piece and you will never part with it. Tube rolling is a joy and yields remarkable and precise changes to fit your tastes and phone needs. I use Grado PS 1000s, Grado Ref. 1s, Ultrasone Edition 8s, and whatever comes in for review. Ultra detailed, quiet as a tomb, superb fit and finish, and neutral open precise defintion. Listen with the new Audeze and be amazed. Or try it with your 800's, and hear near perfection. Reveals everything! It will test your upstream gear. Stock, select tubes that are provided are exceptional right out of the box...you may never tube roll. State of the art.
The Luxman is pleasant and ordinary sounding. The Manley is open, rich and powerful, but not even close to neutral. Not overly quiet as it is provided with cheap tubes. Little flexibility as it is not really supposed to be a headphone amp. Neither are bad and both are cheaper than the HP4...but, the HP4 is so close to perfect that passing on it in favor of either of the other 2 means buyers remorse is absolutely guaranteed!!
I've used headphones for 45 years and the HP4 is worth the effort to afford. Buy it before the price goes up again! It's a Tim de Paravicini designed masterpiece.