Hey there -
I'm very familiar with HOTT and its historical counterpart DBA. I played HOTT/DBA extensively in college (I got so good my foes insisted DBA stood for Defeated By Alex) and competed at Historicon and a few other tournaments. When I was adapting ACKS for mass combat I looked closely at DBA/HOTT, and there are DBA-like elements in the game. However, I ultimately decided the DBA/HOTT model was not the appropriate model for ACKS.
I'm going to attempt to answer your questions, but in the course of doing so I'm most likely going to end up explaining why HOTT's not the right choice for ACKS.
1. Economy: How much does a HotT/DBA element cost in terms of the ACKS economy? I would normally say that each of the companies listed in the ACKS rulebook would equal one element of that unit type, but maybe it isn't that simple?
ALEX: Elements in HOTT are abstract. A Horde, a Lurker, and a Hero stand represents vastly different sized units. Moreover, the implicit scale of HOTT suggests that elements are thousands strong. (You can calculate this by comparing the range of archery fire to the size of an element, and then calculating known number of troops that can fit into a formation of that size).
2. PC Interaction: Normally, I would set up or improvise some specific battle scenarios that could occur as the battle swings one way or another or moves towards specific landmarks or objectives (for instance, if a Church is within an inch of a fight, maybe the PCs must defend it from looters).
ALEX: The entirety of a mid-level band of heroes would appear as a single Hero element in HOTT. Alternatively, very high level PCs might appear as Hero, Cleric, Paladin, or Wizard stands in HOTT. The nature of HOTT combat makes this feel very unsatisfactory.
3. Magic: This is the big one, as an element isn't really a set number of HP or HD in HotT. I could just have the wizard casting spells as part of the 'battle turn' I mentioned above, but I like the way Alex is thinking, with wizards acting in units as artillery or as personal guns for an individual element (he is really on to something with the Napoleonic approach, although it is looking to be more detailed than I like).
ALEX: HOTT's inability to incorporate magic into the battles is the main reason it's a bad choice for ACKS. To give you an example, in our home campaign, we recently fought a battle in which a defending army guarded a river ford against a rampaging force led by a powerful wizard. The battle involved (a) the evil wizard using Lower Water to allow his units to cross at unexpected points, (b) the defenders using Dispel Magic to restore the water level and drown enemy units crossing the river, (c) the evil wizard retaliating by using Move Earth to carve a canal into the defending formations, flooding them, and (d) the defenders retaliating by locking down the attacking units in Growth of Plants vine-barricades. You simply can't have that sort of thing happen when using HOTT.
ALEX: A final problem with HOTT is that at the end of a HOTT battle, you have no idea what your casualties are. The game offers no way to know whether a unit was attrited, destroyed, surrendered, etc., and since each fight is an all-or-nothing die roll without any accumulating effect, you can get outcomes that are very very strange ("No casualties at all this battle!")
If you are experienced enough of a wargamer to be able to play DBA/HOTT, you honestly ought to have no trouble playing DAW: Battles. The two games take about the same amount of time to set up, and ACKS battles don't take very long to resolve - we usually can incorporate 2 mass combat battles in a given game session without an issue, so it's 1.5 hours, basically the same as a HOTT battle.