Tube integrated with real bass. Does it exist?

+1 to the Prima Luna Dialogue Premium integrated with KT-150's. Unless you are a pipe organ enthusiast you will do just fine. If you want accurate bass below 30 hz, plan on spending the cost of a small cottage

Give Mapleshade a look. There are some HH Scott integrated (EL 84 tube) amps they modify that may fit the bill. Read their description and user comment sections.

Jadis DA60 integrated has absolutely impressive low-end slam.

It's a honey of an amplifier. I've own/ed a lot of amplifiers, tube and solid state. Top to bottom, it's the best I've had in my system.

I would guess the DA88S replacement would follow-on in regard to its bass.

I have never read of Jadis having great bass. Have I read wrong things or they improved in this area?
Some used to call Aronov amps Jadis with bass.

+1 on both Rogue and Atmasphere. Great bass is non-negotiable for me and both really delivered with APPROPRIATE speakers.