I have been able to get your data to work with one minor change. The problem is that your TAB files have invalid polygon structures in a few places, mainly with overlapping island areas causing the problems when cropping. I have been able to get most of this work without any changes just by modifying the cropping to not crop to as large of an area. I have placed a new build at
http://www.globalmapper.com/global_mapper10.zip with the change for you to try. Simply download that file and extract the contents into your existing v10.xx installation folder to give it a try.
However, this still doesn't help if a Google Maps tile boundary goes right through a bad part in intersecting islands. For example if you look near Slidell, LA, you can see 2 island areas that overlap. If you edit one of those so that they don't overlap, then export, that tile should come out fine, whereas it was blank prior to fixing it.
Let me know if I can be of further assistance.
Thanks,
Mike
Global Mapper Support
support@globalmapper.com