FW trailers have vented battery boxes in the storage compartment from the factory so it obviously works just fine. The upper vent must be a minimum of 6" above the top of the battery box. If you have an enclosed underbelly, I would avoid having the intake on the bottom simply going into cavity. It is possible in some conditions (temp. & pressure differential between inlet and outlet vents)to have reversal of the air flow and you don't want hydrogen to get into the enclosed space and back inside the TT. Getting the vent 6" above the box may be difficult under the bed. The MTS box is 10" tall you would need a minimum of 16" of vertical space.
A problem with the sealed battery box that is used in RVs (as in the photo) is that it is a bit of a PITA to check fluid level in the batteries. They used to have the upper piece held in place by nuts/bolts all around but they have at least changed that to clip-on fasteners. Still, not the simplest to get off, put back on and to ensure the foam seal is okay. And if you are mounting the boxes in a not-so-easy location to access, it will make it even harder to check the batteries.
I would definitely use sealed AGM batteries for this. You would need to confirm that your converter is compatible with AGM batteries. AGM batteries can off-gas if overcharged so I would still use a vented box for them.
You could consider installing a new exterior door to access the batteries so that they are easier to get to. Doors are available here for example:
Challenger DoorBefore you do anything, if it were me, I'd go to a scale and temporarily sit the batteries in the rear of your TT and see how much the tongue wt. actually does change.