The main problem I found is that Unknown Armies' sleek and fast ruleset bogs quickly when archaic weapons get involved. Simply put: their archaic armor rules suck, because they require way more bookkeeping than anything else in the game. And they slow down combat significantly, because hits now do way less damage. (As I write this, I wonder if archaic armor ought to just impose a flat negative shift on enemy attacks. Or, even better, it works thus: When taking damage from a melee attack, a wearer with light armor ignores the lower die, and a wearer with heavy armor ignores the higher one. So, if some dude punches you and roll an 18, somebody in light armor takes 8 damage, and somebody in heavy armor takes 1 damage. Armor can still knock off weapon bonus damage if you want, but I'd keep it as a flat -3 and -6 rather than tracking what damage type it is. Less bookkeeping is superior to more in Unknown Armies.)
So, instead of adapting D&D to Unknown Armies, I've been thinking about going the other way and adapting Unknown Armies to D&D. Specifically, the other early modern variant — Lamentations of the Flame Princess. It already has fast combat resolution and early modern flair, including guns and early modern armor.
For Lamentations of the Unknown Armies, there are only three classes — Fighter, Magic-User, and Specialist. Magic-users can use both cleric and magic-user spells. To offset rarer healing, and keep with UA's typical action economy, maybe there's a First Aid or Heal skill for Specialists — using it just after a battle lets you heal a hit die roll's worth of hit points, and the rest gets healed by natural healing.
If you want to port the Madness Meters over, everything works just the way as it does in UA2, Chapter Five: Madness, pg. 64-71. Stress checks are Wisdom checks — roll a d20 against Wisdom. If you get lower than the stat (or equal to it), you gain a Hardened notch. If you get higher than the stat, you gain a failed notch, and panic, paralysis, or frenzy as normal. (There probably aren't many therapists about, but if you can find a sin-eater of some sort around, the Referee can give them a score between 1-20 to act as a psychotherapist.)
Avatars bear special noting: an Avatar path is a new ability score, from 0-20. Most people start with 0; your Referee might allow you to start with a couple of points in it if you want. (Maybe you can sink Specialist points into the Avatar ability?) If you seek the Avatar path in-game, it takes nine in-game weeks to gain the first point, and another five in-game weeks to gain the second point. Once you hit two points, you gain another point each time you level up. If you break your taboo, you make a taboo check. Roll 1d20 — if you roll equal to your Avatar score or below it, you lose a point in your Avatar ability. If you roll above your Avatar ability, nothing happens.
Avatar scores directly convert from the Unknown Armies book in 5% increments, so you get your first channel from 1-10 points, your second channel from 11-14 points, your third channel from 15-18 points, and your fourth channel from 19-20 points. You have a chance for godwalker at 20 points, and if you're the godwalker, you choose your godwalker channel at that level. (You probably want to check out Ascension of the Magdalene for alternate early modern Avatar manifestations.)
Given the humanocentric universe of Unknown Armies, and the general feel of the setting, certain spells, effects, and adventures probably aren't appropriate, although that's up to the individual Referee. If you want to give characters the option to be a little more versatile, like in regular old Unknown Armies, let them multiclass. (I'd recommend keeping XP requirements the same, so if you're a level 3 Fighter looking to become a level 4 Magic-User, your next level-up will require +4,500 XP, or 8,500 XP, rather than +4,000 XP.) If you determine Magic-Users are the adepts of the setting, start them off with 1 Hardened and 1 Failed notch in Unnatural, and make them go through the same rigamarole (you have to go crazy in a Madness Meter) to become Magic-Users.