It sounds like you might really like the tube sound; in general tubes will give you more warmth and soundstage, in expense of a less little detail, esp. in the higher frequencies, and slower attack/speed. In my opinion, they work great with jazz, piano, and vocals. However, at this price point with tube amps, you will be giving up some of the accuracy you may now be enjoying with solid-state. May I ask what you are currently using to drive your AKGs?
Any of the Darkvoice range will probably give you the warmth and soundstage you may be seeking... still it is really a question of how much of this you would like to add to your sound sig. and at what price. The great thing about tube amps is that you can simply switch out the tubes and completely change the sound sig.
It does sound like you would like the 337, which is the most refined and solid-state of the models, but at the expense of less of a "tube" sound and a higher price... it could be pretty hard to find one used at your budget.
Considering your budget of $400 and if you would rather buy new, the 336 might be your best option... you can pick one up new for around $300 and still have $100 to spend on some really nice NOS tubes. If you find that you really don't like the tube sound, you can always sell it; I've seen used 336's go for around $200-$250 shipped. As far as those who have suggested the 3322 over the 336, for the extra price, I would only hope that it is more refined, but I would be cautious of those who say the difference is very significant or night and day. If you want to go this route, I would look for one used with some nice tubes for your budget.
Have you considered other tube amps at your price range at all?
I've heard great things about the
Audiotailor "Jade", and it does have two outputs, one more tube and one more solid-state. Also, if you don't mind the aesthetics and are comfortable with semi-DIY, the
Elekit TU-882 is considered a great value with amazing sound... the PCB assembled kit is $425. It also has a switch to change between low, medium, and high ohm phones, it uses two 5670/2c51/396a tubes, which I use in my DAC and sound great! Two 396a WE tubes will set you back around $35 to $40 more though...
I hope this all helps with your decision!