Transformers don't work on DC, only AC - you could convert the DC to AC, transform it, and change it back to DC, but that would obviously be losing sight of the point of the UPS itself, and would be way too inefficient, time consuming and costly. (I know you aren't insisting on them, just sayin'.)
These things are passive (the board is mostly for ease of installation - point to point wiring means manual assembly and can have mistakes) so will be easy to change.
if this is 24v then it's 2s4p and you can literally just change the wiring to be 4s2p. You might need to buy a small amount of wire and some crimp connectors to do this as the wiring can be different lengths or can be cut up differently for series vs parallel use. Fuses are probably fine because you're looking for more voltage, not more current, and the 24v model is probably for a lower power UPS than the 48v one would be for, meaning you'll be capable of pulling more than half of the fuse rating. (What I mean there is that if you were pulling the same total power, but at twice the voltage, you would have half the current via Ohm's Law V=IR - if you're pulling more power and you have twice the voltage, you do NOT want to halve the fuse ratings - but you can take the power of the UPS and divide that by the battery voltage for an approximate max load.)
One thing you should verify, though, is how the main connector is wired. Is it wired up for balanced charging i.e. number of wires = 2+(number of batteries in series i.e. 2 or 4) (edited to make that 2+, because one of them is a mains earth which I see in your photo and which makes sense logically), or is it just +/- (possibly using multiple connectors in parallel if the connector has more than 2 contacts, like my Liebert GXT2 did; I think that had 5 contacts for the EBM connector)
Edit 500000: D'oh, the rectangular connector is obviously for EBM chaining, meaning either it has 2 + and 2 - in parallel (for increased current) or it does seem to be capable of balanced charging... You may need to open the UPS and check how the connector is wired if you can't find a datasheet showing it... You would likely be able to use a DMM and check continuity between each wire of the EBM connector and each battery. If you find that each battery terminal goes to a separate wire, you'll need to rewire that on the EBM side as well. If this is not the case, then maybe it's just two parallel connections, and the connector won't need to be rewired.
I've probably been a bit confusing here as I sort of started writing this before finishing inspecting your photos. Feel free to ask for clarification.
Yes, I always ramble this much.