Edward Van Halen and Les Paul were huge proponents of the direct mounted approach. I tend to take a more scientific approach, being a fellow PC tech like you, and want hard numbers and not some touchy feely anecdote about sound.
The touchy feely side of me that is still there thinks that a certain period PAF would get a hotter sound, or a slightly different alnico recipe in a regular pickup, but the techie side of me gets that ceramic pickup ala Vai or active pickup and gets the hotter tone. I can dial in the rest or scale it back if it's too hot.
I look at the numbers and get something quite a bit hotter and then I know what I have to work with. It's almost a waste of time pining over a slight change due to something like a pickup with or without a mounting ring. If you have the time and energy be my guest and carve stuff up and go for direct mount. I have considered this on a superstrat that had only the lead pickup and I thought a really specifically routed out neck channel allowing for a tight fit neck humbucker would give me that position with optimal sustain....that or I could just put in a hotter pickup. I did the latter and got a rather hot "Jackson" humbucker and it was more than a match for the Duncan JB I already had in the lead position. I could go between the pickups clean or dirty and not have to worry about a volume drop. So much in live situations the neck pickup just gets lost in the mix and becomes anemic as a lead pickup, especially with distortion. But mixing and matching with plenty of experimentation allows for a good result without having to remove pickup rings or do something quite uncosmetic. If a guitar comes standard without pickup rings/pickguards like the EVH and Peaveys, then fine but the obsession with removing rings for tone is overrated.
Are you working towards a Masters in Computer Science too?
Anyway, when it comes to music I try to put my mathematical brain on hold... I have to do enough of that in school... even though, at its core, music is mathematical.
I'm more concerned (well, curious) about people's opinions about if there actually is a difference in tone.
I just don't see how it really could make a difference. Not much of one anyway.
I mean, I can see where one anchored to the wood solidly would stop the pickup from vibrating on a set of springs and ever so slightly
alter the way the magnetic fields interact with the alloy of the strings... but would it really be enough to notice? Are some people's ears that good?
I know it's argued here often about wood, shapes, blah blah blah making differences in the overall tone... some say 'yes, it all has an effect', some say no, only 'this'
makes a difference... but I guess it's an argument that can't be resolved because there's no way to make a true direct comparison since even cuts of the same wood from the same tree can be dramatically different. (My Uncle Joe makes a living selling wood, he can attest to that fact.)
So it's impossible to really compare the effect of any one thing... unless you want to constantly 'tear up' your guitar... and none of us wants to do that.