If your looking to invest in new equipment then the answer is to look at PrimaLuna EV0 series. Quality valve amplification with headphone output. This uses the same circuit / valves as two channel to also drive the headphone stage via a voltage divider network to drop the volume to the correct level for headphones.
I was looking for the same solution a couple of weeks ago to drive both my Focal Sopra 2 speakers in the two channel system, and my Audio Technica ADX5000 / Fostex TH900 mk2 headphones. So, it had to perform. £11,000 speakers and £2,000 headphones. And perform it certainly does. This is high end electronics at sensible cost.
I have the EVO400 integrated burning in at the moment, and the combination with the Focal Sopra 2 is stunning. Likewise, the headphone replay. I no longer have the Chord Hugo 2.
This is serious equipment. It is designed in the Netherlands. I was dubious at first with the manufacturing in China, but ignore that. It's built under strict quality control. The constrution is superb.
Look inside at the components and assembly, it puts a lot of other brands to shame. I can highly recommend.
Take a look.
https://www.primaluna.nl/
Those look like amazing amps. I would love to have a tube amp for my speakers. But they also are very expensive even on the used market. One thing I noticed and found odd is that each of their lineups have the same naming scheme. Whether it's a preamp, power amp or integrated amp they are all name EVO 100, 200, 300 or 400. Would it not make more sense to have a different name for each kind of amp?