Looking for a small tube amp (possibly integrated tube amp)... low power, nice sound

Shameless self-promotion: It's above your stated budget but the Decware Torii Mk IV I have for sale would sound fantastic with your Tektons, and it includes a volume control plus a myriad of other adjustments:

https://www.decware.com/cgi-bin/yabb22/YaBB.pl?num=1573444305

Maybe a used Luxman SQ-N10 would work?

I'm lovin' my Primaluna 30 watt integrated.  It's worth at least a look.

While by all accounts I’ve ever seen the RM-10 MkII is a fantastic amp, after taking a quick look at the specs and descriptions of the OPs components, and doing some quick calculations, I believe he would have more of a gain problem with it than he presently has.

First, as far as I can tell the RM-10 MkII does not provide level controls, while the OP has stated that ...

I have a B&K ST-55.2 SS amp with the "gain" dials on the back set to about 30% and am running RCAs directly into it (no preamp).... and even with this small B&K amp, the usable volume range is TINY.

I calculated that the gain of the RM-10 MkII when using its 4 ohm taps is about 7 db less than that of the B&K amp, but I strongly suspect that the 7 db gain reduction is considerably less than is presently being provided by the level controls of the B&K amp at the 30% setting that is being used. To provide some context, on a preamp having a single-turn rotary volume control 7 db usually corresponds to something like 45 degrees of rotation, except at very low settings where volume changes occur more rapidly as the control is rotated.

Also, I thought of suggesting inserting Rothwell attenuators into the inputs of the amp, to reduce the overall gain. However if the DAC in question is the MiniMax Tube & Solid State DAC Supreme, or a similar Eastern Electric model, its specified output impedance is **extremely** high (22K tube; 10K solid state), which would make it a poor match for the input impedance of Rothwell and probably all other inline attenuators. (Rothwells have much higher impedances than several other makes I have come across). And for that matter the 22K output of the DAC which apparently is being used, as well as the 10K output, are not good matches for the 33K input impedance of the B&K amp, at least on paper.

I have no other amplifier suggestions to offer in the OPs price range, but I thought I should point out these facts.

Good luck. Regards,
-- Al

Ditto on the Music Reference RM-10.  I 

@bdp24  +1 on the Music Reference.  That one looks very tempting to me!

There is a real nice used Music Reference RM-10 Mk.2 listed at $1400 on U.S. Audiomart right now. 35w/ch from a single pair of EL84's/ch. If I hadn't just bought myself one exactly like it, I'd buy it myself. 

Look at Cayin various models.