What makes touchgfx Designer projects un-mergeable is the generation of duplicate identifiers (SingleUseIDxxx). Changing these IDs to be unique might make the problem solveable with appropriate 3rd party merge tools.
If we were making a heavier investment in touchGFX Designer I would consider writing a python script to convert SingleUseIdxxx to a screen-and-widget based ID (as described in previous post). It seems likely that SingleUseID has no real significance...
The problem goes deeper than simply merging large text files.The .touchgfx project file is a JSON file, and the usual source control merge strategies are geared toward code. There seem to be solutions for merging JSON out there, so that would be one...