To make the 55-0-55 part of the system true reduced-low-voltage, the centre-tap of the generator output should be referenced to earth. There should be no connection to the centre-tap of the transformer otherwise circulating currents will occur unless the voltage symmetry is perfect. However, the interwinding screen, if there is one, should be earthed. This would mean separating any internal connection that might exist between the screen and the CT. The screen would otherwise be at an 'artificial' neutral held halfway between the two live conductors by the transformer itself. Not a big deal but not technically correct. I can't see any advantage to making this part of the system 110V TN.
The two sides of the transformer are electrically separate so it shouldn't matter whether the earthing systems are interconnected or not. The output of the transformer, with N-E linked, is regular TN-S so that just needs an earth reference as well.
Are you providing thermal protection to the transformer, and if so, how? Is the 5kVA rating intermittent or continuous? (just trying to visualise the tranny). How close has the output voltage worked out in practice? I'm expecting some contributors here to be thinking that this is a cheeky way to get 230V but TBH it's the sort of thing I would do so I'm not shooting it down!