I wouldn't especially recommend the Conductor as DAC, since I think that just another single bit sigma-delta conversion chip implementation, regardless of its discrete component amp section. I would strive to support the HPA-21 with at least an off chip FPGA interpolation filter DAC, such as a Chord, if possible. The upcoming Schiit Yggdrasil DAC has discrete multi-bit R2R ladder conversion, as well as DSP algorithm bit perfect interpolation filter (~like FPGA). So I'm excited about its potential.
Nothing but the best supporting cast for the HPA-21, eh?
EDIT: On further reflection, I better understand what you meant. A stand-by integrated amp for if/when the Bakoon finally cuts out. Hmm... May be entirely subjective, but I somewhat thought that the Grace 900 series might be a quality setup. And you can prolly pick up a 901 or 902 for cheap, if the 903 is a little rich for you for stand-by mode.
I use a Soloist amp in my desktop setup at work, and while I really can't complain, the Burson seems to me a little too bright (fatiguing) with some headphones, and its chief claim to fame seems to be its 'moar power'. I mostly have to use the first 1-2 click positions on the stepped volume attentuator for headphone listening. Hardly ideal, as maybe it's optimized for its pre-amp function or orthos.