Fortunately, you are using for the Free Shipping >= 350 the shipping module Free Shipping Options freeoptions ...

This means you can customize the one file:
/includes/modules/shipping/freeoptions.php

to manage the Products that are making up the 350.00 that it is looking for to give the Free Shipping ...

Now for a few questions ...

On all of these Product where the shipping is not suppose to be part of the $350.00 ...

They are in Categories ... if they are in Category with categories_id 27 ... would the master_categories_id of all of these Products also be 27?

The question being, for each Category's categories_id does the related Products use that as the master_categories_id ...

NOTE: do not look at the Parent Categories ... be sure to look at the immediate Categories that hold the Products themselves ...