OK, this is a quick sketch of how I think you'd need to wire things up.
View attachment 63227
it should be fairly self explanatory. You need a 3 pole changeover (c/o) switch between your meter and the DB to switch between the L1,N,L2 of the mains and the L1,N,L2 from your generator & transformer combination. To give some change of making breakers trip in the event of a fault, you need to earth your neutral point - without it, a (say) L1 to E fault will simply make L1 "earthy", N at 110V, and L2 at 220V relative to earth. This means that various things a user might expect to be "earthy" (such as the outer screw contact of a screw in bulb and it's holder) will be live.
Consider also fitting an RCD (GFCI ?) between the transformer and the c/o switch (it needs to be on the c/o switch side of wherever you connect the earth to the neutral).
Where does your supplier earth get split from the incoming supply ? In the UK it is in (or close to) the supplier's fuse holder (a.k.a. service head) as shown by the dotted line.
And do the earths to the two DBs have cores separate to the neutrals, connected to a common earth terminal near the meter ?
What I'm getting at is, do you have earth cables/cores from one DB, to a common earth block near the meter, and then to the other DB - and which are at all times separate from any neutral cables/cores (i.e., if you imagine you removed every neutral conductor in the system, would the earths still be connected) ? If you do then you already have the two DBs bonded together. If at any point the cable/core is shared with the neutral then for safety I'd suggest a separate bonding connection - otherwise you run the risk already mentioned with faults in the neutral of a shared neutral & earth conductor, which can make all the metalwork in an installation be live.
To recap on some earlier bits no I;ve had time to sit down and doodle ...
Without the transformer, this is effectively what you have
View attachment 63228
See how the loads on the two sides of the board are now in series, with nothing but the relative size of the loads to determine how the 220V is split. I think you got this, but as they say, a picture paints a thousand words.
A bit more on what I said about switched neutrals when you were asking about not having any 110V loads connected. You'd need to use a 4 pole c/o switch and separate neutral bars like this
View attachment 63229
Notice that when running on the generator, there is now no neutral to any of the 110V loads. BUT, the c/o switch is effectively turning everything off by cutting the neutrals. This means that all the neutral wiring, wiring that should be made "dead" by switching off, both pins of sockets, the outer screw body of lamps and holders, etc is live - when users might be assuming that they are dead. It should be fairly obvious now why such an arrangement is explicitly prohibited by UK wiring standards, and even if it's not prohibited by yours, I would strongly advise against such an arrangement.
As to transformer rating.
The very worst case is zero load on one side of the board, and a high load on the other. In this case, both halves of the transformer winding are carrying half the load current. E.g., if you had (say) a 10A load on L2, then the transformer would pass 5A through the upper winding from L1 to N, and by transformer action, another 5A would pass in the opposite direction from L2 to N - thus producing 10A out from the neutral connection. The generator would just see 5A load across 220V (= 1100VA). The transformer is handling 5A x 110V x 2 = 110VA; that's 5A in each winding, 110V across each, and 2 windings.
If you (say) added 5A of load from L1 to N, then that would supply half of the 10A needed for the N-L2 loads. Thus the transformer would now supply 2.5A from L1 to N, by transformer action push 2.5A from L2 to N, and thus supply the 5A from the neutral terminal to balance the difference in load currents. The generator would see 7.5A of load at 220V (=1650VA). Note that the transformer is now only handling 2.5A x 110V x 2 = 550VA even though your are running 50% more load.
I had to "refresh my memory" on transformers to get my head round the details for that ?
If you have any difficulty getting a 220V centre tapped autotransformer, then a 110V-110V standard isolating transformer would do equally well - connect N of one winding to L of the other winding and you have a 220V centre tapped auto-transformer.
In theory you could apply all your load to one half of the board = and thus need a transformer rated for the full generator output (8kVA). In practice, that's unlikely as your 110V loads will be split across the sides. Also, your 220V loads will not use the transformer at all.
I'm not sure how auto-transformers are rated - I assume it's for the total load it is running (e.g. 1100VA in the first example above. An isolating transformer is rated on what it can transform, but when connected as an auto-transformer like this, each winding is only carrying half the load - so you'd only need one rated for half the load, i.e. only 550VA for the first example.
So possibly some thought needed as to what is a realistic rating you need - it won't be 8kVA to match the genny.
lastly, I've hinted at this previously. I have no idea what your wiring regs/codes over there have in them, nor what requirements there are for qualifications to carry out this sort of work, nor whether you might have to notify someone of the work. You would be strongly advices to consult someone local who does know what's what in terms of both safe practices and your local laws/regs.
I.e., treat the advice you've been given as what it is - advice from "some bloke on an internet forum".
Simon