I've just gone through the expense of replacing a <1yr old Hy5 Gen 1 with the Gen3 to solve the same issue as the OP: the 2.6KW AC output of the inverter wasn't enough. I now get 3.6KW which is better, but I wanted to get to 5KW peak at least, and preferably to 7KW (so EV charger can work at near-peak).
I suggested all the options I could think of to get to 5KW: AIO, AC3, 2nd HY5, etc, but the installer wouldn't do any of them. Because GivEn don't support the AC3 and HY5 in tandem they were out, and the AIO has a max distance (1 metre?) between it and the main power inlet, and for me there is literally nowhere it could be fitted safely. (My current install is about 12 metres from the power inlet point, which is perhaps not ideal but then life isn't!).
I would concur that GE need to up their game, given the state of play ideally use the 6KW circuit from the AIO and unbundle it into a HY6 with true 6KW AC output. it would make a good addition to their product line. Properly supporting inverter combinations: HY+AC, HY+HY at least, would help alleviate the issue.
However, I did speak to someone at GE support and was told bluntly that this was very unlikely to happen in the next few months at least as other projects were scheduled.