If you want to keep “all things equal” but assess the effect of tubes in a balanced preamp, a good solution would be trying a Schiit Freya+. While not particularly cheap compared to Douk stuff, it lets you try 4 different configurations and see what you like best. You can run it passive, with a JFET differential unity-gain buffer, with the tube differential 4 dB gain, and with LISST tubes which give you a differential MOSFET 5 dB gain. You can also try turning up the volume on the Schiit and using the Topping to do the level control or vice-versa.
The benefit of that is you get to try several different things. The downside is that you’re still running the signal through 2 preamp stages, as the preamp stage of the Topping can’t be bypassed.
It can be done. You could use a switch like this:
And if you want “balanced all the way,” use an XLR splitter cable, something like this:
It would eliminate the signal altogether. You can’t turn off the tube influence that way. You can turn off the tube influence by running the Schiit Freya+ in one of its non-tube modes.
Let me suggest a different tack, assuming you’re just trying to dabble a little bit with tubes to see what all the fuss is about without spending a ton of money. Run the single-ended outputs of your Bifrost to a Schiit Vali 3 and compare tube hybrid to the solid-state Topping. You might decide you like both for different reasons, you might decide you prefer some headphones with one amp and other headphones with the other, who knows? In any case, you haven’t spent that much, and it’s a much cleaner comparison than the options above. Even if you don’t like it at all, you can return it and only be out about $20.