I've got what I believe to be a TomTom XL version 2 (XL not One XL), which won't pick up any GPS signal. Obviously there's not a lot I can do (tried GPSQuickfix and restore to factory, apparently it's been back to TomTom before and they couldn't do anything with it but I don't know if this is true). It's a 4.3" screen - Looking on eBay, devices of this size with cracked screens appear to be going fairly cheap. So what I'm asking is, are there any models other than the XL version 2 that share the exact same screen (i.e. I could swap my working screen into them)? Any help would be appreciated.

On the GO series TT uses two slightly different screens.
One of them is also used in some other 4.3" models.
The important thing is the location of the connecting cable and that the serial number for the screen is a match - the last 2 digits are not that important and can differ.

If you opt for the same model TT your screen will fit as a replacement for a 720 or 730 you still have a 50-50 chance.
You can take your TT apart, check the number on the back of the screen and check on Ebay for it.
If the same number is used for more than your model you should be able to find out this way.