Beware of trapping your jack, tire iron and whatever else you have in the below deck cubby.
Perhaps mount the slide on a raised platform that is just tall enough to clear the cubby door as it opens? Marine plywood and paint to match the carpeting or cover in oem carpet...
If your platform spans the cargo area then you could attach the side verticles for the platform to the tub in a manner similar to Best Tops' Flexa Trunk. Here's a link to a Quadratec page that has a link to the install directions for the Flexa Trunk. I have the Flexa Trunk and it does mount to the tub at the wheel wells, so adapting Best Tops' direction ought to work. The Flexa Trunk is just about the correct height, btw, a 5gal bucket slides under...
I have a small ~16qt Engel that I keep behind the passenger seat most of the time, so I can reach it while driving. It's the best Jeep mod going! No ice, cold beer, sodas. Use it for lunch makings too. Holds about 18 drinks packed well, or lunch and ten to a dozen. The small Engel doesn't have a low voltage cutoff switch, so I use one between the fridge and the cigarrette lighter. With my one Group 31 Blue Top Optima, I have to run the Jeep every other day to recharge the battery to keep the drinks cold. I have a larger 60QT Combi for more extended use, it takes up most of the cargo area though.
JPK