For me the big things to simplify are battles and adventures - both can be sucking quagmires of DM time and have really slowed things down in the past - particularly forum adventures.
I'd suggest making armies smaller, having an outset die rolls to dictate how badly/well people do and each person issue a paragraph or two summary and then run each "chapter" of a battle by simple DM fiat - a big battle might have 2-4 chapters, most however have only 1 or 2. Lack of communication with generals was a common issue in medieval war anyway,
Adventures, most could hopefully be run as simple actions/outcomes - there was a die-roll outcome sheet that arpig did. Only the bigger adventures would then play on the forum / over email.
Rules - keep the same, it saves fiddling the sheets and they aren't the big issue, particularly for the veteran players.
Turns - no more than 1 a month, and preferably 6-8 weeks - that was enough to keep RoE II alive and leaves people plenty of time - in practice the problem for players was prolonged time in purdah waiting for turn resolution but if we expect a longer timescale from inception that's less of an issue - but I'd add a DM rule - no big stuff in the week prior to submission, if you have a bomb to drop, do it in week 1-2 or wait a turn, the post-scrummage issues tended to occur when something blew up at the end, some players had already submitted, others had RL issues, and suddenly a months worth of diplo had to be done in 2 or 3 days - and if DOs are getting hastily re-written then they are more likely to be incoherent, full of errors, etc and thus take longer to process.
I'd co-DM if people wanted me too, I'm not hot on the rules but I've got time.
As a minor point, the P&H is a real hog, if we cut down I'd suggest cutting down peripherals a lot, so if we do Rjurik then the north and west coast of Anuire are in but the rest would be cut off, we could do a single "Brecht sheet" for holdings in a few provinces if people wanted but the bulk would go.