A stock Burson buffer is not up to the sound quality of the modified SB, and doesn't give you enough gain anyway. You may be able to improve things by getting some short, low capacitance IC cables to reduce the load on the DAC, but your gain will not increase without an amp stage.
What you really need is an active preamp that makes 20dB+ gain. This is exactly what a preamp is for, and will give you silent, good sounding gain to compliment your great source. Contact Steve Sammet of SAS Audio. He can explain why a real preamp is the best way to solve your issue, or just read articles on his website to get the concept.
A Eastern Electric Minimax is a great sounding tube preamp with the gain you need. Used for about $600, or new with importer Bill O'Connell's excellent support. I have not found a solid state preamp at this price range that retains the subtle musical qualities of a source as good as Wayne's SB, not many at high prices either. For small signal gain, tubes are the way to go, IMO. One of the best tube preamp circuits out there is Aikido, which you build from a kit. Good quiet power supply is essential, so good tube preamps are not as cheap as SS.
Good luck!
Rich