As stated, there is no way to officially upgrade capacity, and anything you do over rated capacity is at your own risk. The rest of this is to aid in controlling a 4,999.9-lb trailer with 499.9-lb tongue weight. I'm not advocating going over weight in any way.
One huge factor is where you'll be driving. Apple Valley is mostly flat if I remember correctly, but if you're dragging this beast of a trailer around sharp curves up in the nearby mountains it could cause lots of problems.
Handling: In addition to better shocks, get either stiffer springs (ride will be horrible when unloaded) or airbags (much better solution). Stiffer tires, either in the form of E-rated sidewalls or larger rims with lower-profile tires, will help noticeably with curve control. If anyone ever makes an upgraded stabilizer (anti-sway) bar that would help. If you have a lift, get extended rear links to bring the stock stabilizer back into proper alignment.
Power: About the only proven bolt-on way to get more power out of the 5th Gen is to install a more free-flowing exhaust in the form of a URD Y-pipe and catback muffler. After the exhaust a more open CAI (TRD Pro or K&N) may also help just a tiny bit. You already mentioned coolers. Regearing to 3.91 would also help, but that's a huge expense for a small improvement (stock is 3.73). The next gearing option is 4.56, which would kill your road mileage and be a waste unless you also upsize the tires for off-roading.
Stopping: The 5th gen already has massive brakes, but most definitely you'll need an electronic ttrailer brake controller. Surge brakes (found on most rented trailers) help some, but at the weights you're talking you want active brakes on the trailer.
