This is a perfect example of why we need ranked choice voting. I think #BD60E2 is best, but due to its unpopularity I'm forced to vote #BD60E1 if I want my vote to matter.
Idk if you're serious or not, but this site actually does ranked voting: you don't get to choose your favorite color out of 17M, but you rank pairs. The problem here is that you can vote a variable number of times. I guess it's possible to come up with different algorithms to determine the winner.
You'd need some algorithm that works on continuous variables, that is, #44E205 should rank closely to #44E106. Somehow you need to learn a function over rgb sampling only some of the points. Maybe you average over votes for colors that are close to a color in rgb space.
16 million collars aren't that many compared to large-scale internet systems. If you got 160 million+ votes you'd start getting meaningful results without any averaging.