Mgcv has a hard time if your independent smooth variables are anything but randomly distributed. Honestly, I would just use a random forest. Then all the interactions are naturally incorporated and you aren't committing to linear relationships with lat and long.

How are you fitting your GAM? Maybe some regularization is needed? Are you wedded to GAM? A Random Forest would be self regularizing within the sample outcome ranges.

If you can't afford the application, you definitely can't afford grad school salaries.