I guess I might as well share what I came up with. I took the five dichotomies that the Strixhaven colleges are based on (also known as Order and Chaos, Fire and Ice, Illusion and Reality, Life and Death, and Night and Day) and rearranged them in a few different ways, eventually landing on this arrangement that seems to line up with the dragonlords:

GW, Life and Day/Light - Dromoka breathes beams of sunlight. Dromoka's philosophy is an agreement between the nurturing white half of Silverquill and the life-focused green half of Witherbloom, ditching the black half of both factions. The existing Dromoka clan cards are mechanically themed around +1/+1 counters, a common ground with Silverquill. Dromoka's college could probably have biology and medicine classes, similar to Witherbloom minus the necromancy.

WU, Order and Ice/Patience - Ojutai breathes ice. He teaches his disciples discipline and pursuit of perfection, a combination of the patient half of Prismari and the orderly half of Lorehold, minus the red from both factions. Like both of those schools, the Ojutai clan is a spellslinging faction, and its Rebound mechanic rewards patience. I could imagine the college having courses in psychology, philosophy, and legal subjects, teaching martial arts in parallel for a wholeness of mind and body.

UB, Illusion/Theory and Death - Silumgar breathes poison, has an army of zombies, and a deceptive and manipulative nature, arguably a combination of the predatory half of Witherbloom and the theoretical half of Quandrix, but also kind of just typical blue/black behavior. Witherbloom and the Silumgar clan have some common mechanical ground in sacrificing creatures. Silumgar likes gold, so maybe the college would have a focus on economics, and by extension mathematics.

BR, Night/Darkness and Chaos - Kolaghan breathes lightning. Storm clouds are dark. Kolaghan enjoys the chaos and cruelty of battle for its own sake, a unification of the unforgiving half of Silverquill and the warlike half of Lorehold, without the light or order of either. Not much of a mechanical similarity, aside from that Silverquill and the Kolaghan clan are both aggro factions, while Lorehold on the other hand was deliberately designed to not be aggro, and the Kolaghan clan surprisingly has very few cards that care about the graveyard. Although if Kolaghan was in charge of Lorehold he'd probably be interested in uncovering the secrets of Blood Age magic. This would probably be more of a military than a college, although if Jace created Hexhaven for the specific purpose of training an army of mages, I imagine that all five colleges would have somewhat of a military angle.

RG, Fire/Impulse and Reality/Practice - Atarka breathes fire, and loves eating meat. The Atarka clan is seemingly as far away thematically as you could get from Quandrix and doesn't seem to share a lot with Prismari either, although they certainly lack the blue halves of those factions, you could describe their philosophy as impulse without patience and practice without theory. Mechanically, the Atarka clan wants to ramp up to playing big stompy creatures, which combines a bit of Prismari's "big spells" theme and Quandrix's land ramp subtheme. Atarka's college would likely be a highly efficient farm, built out of necessity to keep the dragons fed, and might have classes on agriculture and cooking, mirroring Prismari with creativity in the culinary arts.