Glad that you pointed out that the 5691 is a beefy 6SL7, not a 6SN7. The 6SL7 will probably not harm the DAC but it does not have the exact same specs and also has much higher gain. I have found that 7N7s and Tungsol black glass 6SN7s (with the round(oval) plates - TSRP) were the best in other equipment that I have own. The Tungsol TSRPs are very expensive in the 6v version but a steal in the 12v version.I strongly recommend you to try rca red base 5692 tubes cause they are the substitute of 6SN7 tubes, 5691 tubes are not. 5691 tubes can be considered the subtitutes of 6SL7’s. I used rca red base 5692 tubes, they sound very dynamic but a little aggressive for me. I prefer tung-sol vt-231 smoked glass, oval mica, copper posts or marconi B65 to rca 5692’s. rca vt-231 smoked glass is an economic alternative and 5692 is definitely a great sounding tube on the right equipment.
in the place of stock 5U4G cossor 53KU or gec U52 would be the best sounding options disregarding the unobtainable we274b’s. Cossor GZ37/53KU (GZ 33) worths a try which has an indirectly heated cathode.
I have a Baltic ordered and am going to see if they can make a switchable heater voltage for the 6SN7 sockets(6v/12v). This would open up a lot more rolling options. I have a Linear Tube Audio MZ2 that can take either a 6SN7 or 12SN7 by just moving a jumper. The Baltic has a 12AU7 on the output so it has 12v already. It would just need a transformer that can provide enough current for the other tubes.