Upon further review, if the manufacturer of the module states they can be load shared, I have the following suggestions.
1) Remove the connection to TRIM, let it float, the UCC39002 is intended to adjust the Remote Sense (S+) of a module.
2) Following figure 4, High Voltage Application in the data sheet, the collector of the NPN should be tied DIRECTLY to the S+ of the module.
There should be no series resistance like your schematic shows.
If this does not allow proper function, or at least improves it, we will need more answers from the module manufacturer.