I once ran a whole BECMI campaign that took two players from 1st level up to the end of the "Initiate" tier (immortal level 6th in Wrath of the Immortals, roughly equivalent to a Temporal Novice in the much more baroque gold box rules) over the course of about three real years.
When the Companion Set rules kicked in, I started them off by introducing module CM1: Test of the Warlords and having the PCs engage in the Norwold "land grab." As a rule, I don't like published modules, but I recall CM1 being both great fun and a good introduction to the various Companion level mechanics.
The domain management rules have always worked well enough for me that I tend to stick with them as-written (I don't have to stoop to importing anything from ACKS), but the War Machine isn't great. You can get the same results at a similar level of abstraction, and with far less tedium, by just using the core battle mechanic from Risus, treating each salient feature of a given army or navy as a "cliché." And if that doesn't satisfy (which, IME, it won't), you can go with either Delta's Book of War (which is great, especially with ChgoWiz's "Fellowship" rules tacked on) or (my current preference) convert the mass battle rules from Decipher LotR's Helm's Deep supplement.