The LP can sound more “tubey” with the right tube, but it’s an expensive tube to roll, I haven’t really played much with my CTH and tubes.
You could try the Schiit amps or the TA10/20.
A lot of people seem to think that tube amps should be in your face wet like the dark voice.
FWIW Most good tube amps don’t sound like that, they present as good clean sound usually with some additional mid/low end richness.
If you want a tube sound you probably want a tube amp, and that (unless you get into higher end amps) usually rules out planars.
A HD600/6xx/650 and a Bottlehead crack with Speedball is an astonishing combination if you can run to it.
In other reasonably priced tube amps to pair with a HD600/6XX/650 I really like the the SW51+ and EC ZDT Jr is pretty nice, but the SW51+ is completely unavailable and the ZDT Jr you have to find used, and deal with the potential hum issue.