I'll be the wet blanket.
I don't think going from one table to the next is a good idea. Having a player have to split their attention will slow things down for an already huge game.
Having the side tables affecting the big table is probably the easiest mechanic as the games will be going faster on those tables by default.
Not fair! I was going to be the wet blanket!
I can see a standard approach to handling all bombardment interactions. If at the end of a given turn some set of objectives is controlled by a given side on a given table, they enable the table captain of another table to do this or that thing which would play as a stratagem. Simple enough.
I would limit it somewhat. I once attended a Dakka Dakka battle where the opposition cleanly won the war in outer space and started orbital bombarding the heck out of one table. Not fun being thoroughly clobbered and there being nothing one could do about it. Some interactions, sure, but in moderation.
Moving units from one table to another could be done. I could see interactions between the sewer and city tables especially. Perhaps moves might only be allowed between those two tables. Perhaps if a unit is going to move, it must be unengaged and adjacent to the 'tunnel' exit. If there is no room to place the unit on the other table, the movement would either be blocked or one might come up with inter table assault rules.
Mind you, I am not a big fan of moving units from one table to another. I don't want one player splitting his attention between two tables. At the Dakka Dakka battle, the rule was that a player who moved stuff between tables gave up all control of the unit moved to the other table. One of the players on the new table took over control of the unit. Dakka Dakka also held all their tables in sync time and phase wise. If it was movement phase of turn 3 order on one table, so it was on all tables. This made gates between tables simpler. If each table has its own clock (which I really want as I don't like all tables being slaved to the slowest table) then a unit which leaves one table might not arrive at its destination until the next movement phase for that side on the destination table.
Clumsy. Complicated. However, in the Dakka Dakka battle, the table that got nuked from orbit was strongly reinforced by gate from another table. This turned out to be decisive.
Movement between tables might be tried on one pair of tables as an experiment? Sewer / City seems the obvious pair to try it on?
I'll suggest that the bigger the table, the slower play is apt to be. I note that a lot of the early suggestions here give the side tables an opportunity to make life on the big table more complicated. Some thought might be given to not making things too too complicated on the big table. I think in 2010 the big table only got to turn 3 or 4, while on the Moon Order got essentially wiped out on turn 5 so Chaos unofficially fought each other for a while.
Just for the big table, you might consider a rule that units must stay in or near their own deployment zone. Some of the delays in 2009 were due to players that needed to be in several different places at the same time after bringing units onto the table far from their army's original deployment zone. This resulted in a lot of hurry up and wait. Last year demonstrated that we could play six turns with 10 players on 3 tables, but could not do so with 20 players on 6 tables. We might consider long and hard how to simplify the lives of the 20 on the six. (The simplest suggestion might be to break the six tables into three and three. Keeping the complexity level of the special table rules on the big table comes next. Special command and control rules to keep all members of a given army within a table or two of their deployment zone might be another.)