Not sure about FACS, but what you describe is similar to droplet digital PCR (ddPCR). The samples are still in an aqueous buffer, but they are emulsified in oil, creating many microscopic droplets that each contain some sample and are isolated from each other. BioRad makes a machine that does this, but whatever you are detecting would have to produce a fluorescent signal.

Sorry, just realized this was asked 7 months ago. My two cents though, for what it's worth.

Ok, I understand now! It seems to me that there are some methods that exist to determine the relative age of certain segments of a genome based on how many/what type of mutations have been accumulated, but I am not familiar with these methods. Additionally, you may be able to tease out relative emergence by looking for other organisms that have $T_1$ but not $T_2$ (or vis versa), indicating that certain subsets of the population were exposed to $E_2$ while others were not. But this is getting beyond my expertise. At least I finally figured out the proper mathematics formatting!

"A naive post hoc evolutionary story would simply observe that T2 is advantageous and so was selected for but this would be wrong." This wouldn't necessarily be wrong. T2 was in fact selected for, just at a later time than T1. So it sounds almost like you're after the relative time of emergence/selection of 2 traits? In that case, you could maybe build separate phylogenies for each gene/set of genes, and then compare branch times, but other than that, I'm not sure.