Let me rephrase something I said earlier. Let's say tone is a function of six variables. I just made up that number, so assign them to anything you like. Let's say you want to document guitar acoustics and electronics, and we treat those as variable a & b. c,d,e,f are other independent variables. The dependent variables are frequency response and overtone series.
OK, so we have:
x,y = f(a,b,c,d,e,f)
x and y can be tested independently, so that's not a huge worry. What is a problem is you'll be doing a multiple regression analysis where you don't have data on c,d,e,f. It can be done, but you need a very large data set to tease out the effect of a & b. I used over 100 observations of a single phenomenon in my thesis, it accounted for only 2% of observed variation, but I was able to demonstrate that effect to statistical significance (hooray!
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In other words, you can either attempt to control for things like string age, amp input impedance, and pick attack, or you can just collect enough observations where those differences "average out", for lack of a better word.
So if you set out to determine the difference in types of wood used in LP construction, you could have 100 guitarists play the same music on their LPs into a DI. That's probably good enough IF they all had the same pickups. If somebody has P90s, toss them out right away. If you want to study pickups and wood, you'd likely need many more than that (I don't hazard a guess because I don't know the varieties of LP construction that well).
Your problem is you want a comprehensive database of all guitars and all options for those guitars. So you'll have an incredibly difficult time getting enough observations of each model to generate statistically significant data.
Instead, you could scale down to the typical shootout approach: "here's what each of my guitars sound like when I playing them similarly but not exactly, one at a time". Enough such anecdotal observations can be useful, but it does require every listener to listen to all of them. That's the disadvantage of the anecdote (and the advantage of the expert luthier/player/whatever).
PS the effect of pick angle, type, placement of pick relative to neck/bridge on tone is VERY large. Think about classical guitarists (who don't use picks!) and how they generate a range of tones arguably larger than a typical electric guitar's difference in neck/bridge pickup response. mutts will be quick to tell you that tonal difference is a measureable change in the instrument's overtone series, which is what you are also trying to study with different types of guitar construction. And when you think about it, the picking action has a much larger effect. Which is brighter, a LP picked right at the bridge, or a Tele at the 12th fret?
Seriously I teach this stuff at degree level, well up until recently I did and I also have 30 years in the trade building and repairing guitars and stringed instruments. I would never discourage people from exploring these things, heck I've fallen for the same thing myself in the past and got distracted from the real purpose behind what we do and that is make good and enjoyable music. 
