Since you seem to put a lot of stock into the methodology of your research, I will point out that your last example - comparing two solo runs - is a qualitative study, not a quantitative one. All you can empirically say by comparing two data points is that one is faster than the other. You can, of course, draw inferences as to why that might be, and you do that; nothing wrong there! But you are running scenarios in your head and coming out with a most likely explanation for the discrepancy in time, not having your data back you up. Again, I do not mean to say you are wrong in your approach, only that it is not a quantitative, but rather a qualitative, one.
A quantitative analysis implies a number of empirical cases (in this case, runs), through which you can build confidence intervals and test your hypothesis: in this case, that weapon A is more powerful than weapon B; as many people, including you, have mentioned, there are a number of variables that cannot be controlled here: player, map, objective, ... each of those variables would need an additional set of multiple runs to be included in a quantitative analysis, before you could make reliable statements about your hypothesis; in other words, a purely quantitative approach to this problem is quite simply impossible to achieve IMO, at least with the resources at your disposition.
I am also a bit confused as to what you are trying to say... are you now referring to the acolyte's influence in solo runs, or in pugging? Your argument started in reference to the latter, but seems to have moved to the former. They are, however, quite different beasts, and I don't think you should mix them up. People approach them differently, as they impose different requirements on kits, loadouts, and playstyle: you yourself point out only few runs in the solo HoF include Harriers, and yet I doubt I am the only one who sees Harriers in most pug lobbies.
Additionally, only a sub-population of those who pug also does solos and speedruns - so you are dealing with a (likely) skewed subsample of the entire population (SMR pointed this out to you already btw).
Trying to use data from solos to buttress your hypothesis on the Acolyte's OPness in pugs, on the grounds that it is the only data available to you, does not make it relevant. After all, we don't use rally drivers' performances to set speed limits on our roads 