I’m coming into this a little late, but I’ve a few thoughts, and experiences, which I just note below. It might note be directly relevant for your current plans though.
In Empire I’ve received and responded to IC Email; most often it is PDF by email; although some players delight in creating lovely period looking letters with wax seals etc; which are normally then put in a modern jiffie bag and sent by post. UK post is next day first class ,or 2-3 days second class. PD (the organisers) have rules about what and how plot can be discussed outside of the time-in; so that the game is kept to the field, but mostly what is organised is introduction; copies of documents discussed in the field and attempts to arrange meetings for the game.
In Maelstrom (where I was a plot team member) we allowed players to write to NPCs; and it was a big plot effort to reply to those letters.
In “Love Letter” we encourage players to write letters to each other in the in between the scenes. We try to read them as GMs but that the busy part of the game for the GMs.
In none of cases was plot consistency big issue; both games there are clear boundaries layed out in what the players can improvise. Empire probably has it better documented but they had well over 2200 players last event,
In comparison Love letter is 10-12 player 4 hour game, but equally the players are split into to groups; each sitting together and since both groups have pretty free IC communication during the gaps it is easy and sensible for them to discuss anything which effects other characters which goes in their letters. We (the GMs) often get sanity check questions from the players as well about what is sensible for them to have done, so it works out simply in that case. Obviously that isn’t quite what your talking about but a mechanism to IM the GMs would probably achieve some of the above.
In Maelstrom I believe I saw letters which related what happened on the field in way very different to my on-site perception; but unless the NPC had a contradicting letter; they was no reason for them (the NPC) to believe otherwise.