You are right, you need to be extremely careful before using longer screws. The maximum length of the screw below the bottom of the table base is 3/4 inch given the floor thickness and carpet thickness. Otherwise it will go thru the waterproof cover and also damage the seal and possibly the main floor when the slide is retracted.
You do need to check the integrity of the floor. Water leaks at the bottom of the side wall can soften the slideout floor and let the screws pull loose.
You can try adding more screws than just the two that is typically used. This would require drilling other countersink holes in the base. If you are strapping the chairs to the table, the extra mass of the chairs may be working the screws loose while on the road. If so, you might add some D-rings to the floor and strap them independant of the table. As a last resort, you could use bolts completely thru the floor with the head down, these would need to have an extremely flat head (there are some carriage bolts with a flat head but they require a square hole). This would need to be caulked as well.
Larry Day, Texas Baptist Men volunteer
'13 Silverado LT 3500HD D/A CCSB 2wd, custom RKI bed
'11 Crossroads Cruiser 32MK loaded