Refractometers are no good at all, especially with THIS much colored stuff. Could get over 2x error, which is nonsense.
After all, you don't have to lose that stuff, if you had a tall and narrow plastic cylinder, that would fill that glass on the photo when you are done.
I was thinking to design and build a U-tube density meter for regular people who can't realistically spend a few thousands on proper tool, I can see those in slightly above decent refractometer price range (and that would indeed take small amount of sample, not as small as refractometer, but still). I wonder if I'd be able to sell enough to cover the expences (and myself I do have a ridiculously expensive and unnecessarily fancy MettlerToledo U tool in addition to all floaters and refractomters, remaining from good old times I was hoping to do paid analytics for microbreweries and thus needed something certified).
Refractometers are quite useful for pale wort and clear distillation products - or anything where you calibrate close to target phase subspace (honey, must, well-known beer recipe, etc.). I use mine to determine when fermentation rate slows down to determine termination in yeast tests - their relative readings are OK, if they aren't changing, it's worth considering density is stable.
Regarding U-tube, that's fun enough little project if done right. I had even more daring idea to build contactless (read through glass) density scanner, I even have the already soldered and flashed board and transceivers somewhere around the place. The prospect of quick reading density and inner fluid temperature without exposure seems attractive enough, but it's a lot of research work to tune this tool concept, and then to turn it into comfortable product, and I'm kind of short of time-money invariant resource now.