After further listening, much swapping back and forth (which makes it sound less of a pain in the ass than it really is), I have indeed settled on the OPA2107 + LM4562NA (which I'll to shorthand "OPAs" from this point on). Compared to LME49720NA + LM6172 (shorthanded "LMEs"), I lose some realism with some instruments, particularly the piano, which sounds almost lower pitched than it should. Some instruments I actually gain realism, such as flutes, clarinets, and some varieties of bow/string instruments, where the body of the instrument is better conveyed. I lose some of the massively wide space and instrument separation, and light, airy and open sound that can actually seem more refined and higher-end much of the time. For many this would be considered an upgrade, and if it were in the form of a full-size amp, people might spend an extra $500+ on a increase like that. The cool thing about opamp rolling is you can get the same sort of upgrade for like $13, and the beauty is if I ever feel the need to return to that sound signature, I can just open a drawer and whip out those opamps again. For now, the OPAs are staying.
Really though it's simply a difference in priorities and tone. LMEs prioritize the highs more, OPAs prioritize the lows, and both have excellent mids with very different characters. The OPAs have more weight and body, lots of warmth but with an enveloping sound. The soundstage isn't as wide as the LMEs, but it's very three-dimensional, surrounding you with all the elements in the song and extending deep with layers on layers giving an almost holographic presentation. Sometimes it can be a little harder to hear some of the really quiet background elements, like background strings on a pop song, or the plucking guitar behind an orchestra, compared to the LMEs, which sort through all the elements more effortlessly. On the LMEs, nothing is really given much weight over anything else, and this was a problem for some people when it came to voices (which didn't really bother me). The OPAs like to let the more prominent elements be brought forward at full force, so the full impact is felt. Sometimes this makes things sound congested and muddled a bit, but it's not really that big a problem. Bass just hands-down goes to the OPAs. They hit hard, go low, and make themselves known. They might run into the lower midrange a little, but this helps sweeten things up a bit in my opinion. Highs on the OPA, while not quite as prominent as on LMEs, don't draw attention to themselves in any negative way. They're fast and balanced with the rest of the spectrum, and work very nicely with the overall sound. The LMEs put emphasis on the highs, which contributes to their airy nature, but can sound a little unnatural on headphones that don't have the benefit of distance between the driver and the ears to help make decay (a crucial element in realism) more natural such as with speakers.
Overall the warmth and tone seems to get into the "soul" and intention of the music better than the more neutral, technically superior sound. You feel the OPAs more on a visceral level, getting more emotionally involved in the music and, to my ears and with my setup, just enjoying it more. To me that's priority over technical prowess.
The buffer plays a pretty big role here as well. The LM4562 did the most to contribute to the congested nature, but really brought the velvety smooth warmth and bubbly nature to the table that I simply didn't get using the LM6172 as buffer with the OPAs. The LM6172 turned the OPAs into something almost indiscernible from the LMEs: light, airy, with little bass weight or impact, but good instrument delineation, which I thought was strange. The LM4562 with the LMEs helped warm up the mids a little, but did little to change the bass characteristics, which remained tight and less pronounced. With all opamps I have (hardly a fraction of what some people here have), I could try literally hundreds of combinations, but I doubt my patience and the opamp sockets themselves could withstand that much testing, and at certain points, such as the OPA2107s + LM6172 combo, things start to run together and you can't tell much apart anyway. I'd rather not drive myself mad with all the variations.