Hi,
With Pro you will be limited to 4096x4096 image exports. With Basic you might be able to go higher, depending on how much video memory you have. Note that your Pro code will give you access to TF basic as well, so you could try installing Basic and see what you can get.
Our intention is to improve this in Pro, or find a way around. Hopefully soon.
As for Global Mapper, I am really shocked they don't support world files. What version are you using? I have version 7 and see that it isn't supported. Perhaps in the latest?
If not I will make a note to look into the ".prj" format and see if we can add support for it in TF.
Thanks.