I've looked into liquids as damping layers for enclosures... I didn't keep notes but IIRC they wouldn't work well because they tend to transmit sound pretty well.
However, you might be on to something! If you could find a liquid/gel that was highly viscous and also remained transparent (think green glue, but clear) then it would probably actually work fine. Constructing it might be a b**** but there's no reason a layered design couldn't work. It's actually pretty common to do constrained layer damping in DIY speakers using various adhesives that don't solidify. So the trick will be finding one that's clear and stays clear...
It wouldn't be as good as filling the box with wool, but it would be better than nothing. It would also reduce the penalty from not doing bracing.