That's the problem with people trying to use only the MAX tow rating for planning. The max tow rating (3500 lbs) is only available if the Explorer is empty. So you end up having to subtract passenger and cargo weight from that 3500 lbs.
An easier way to thing of things is to start with your GCVWR, which is 8000 lbs for a V6 non-tow-package Ex:
8000-4344? (curb weight of '02 Ex V6 XLT 4x4 per Edmunds.com) = 3656 lbs
3656-150 (standard 150 lbs driver allowed) = 3506 (there is where your MAX rating comes from, but there is nothing in the truck yet).
3506-3500 (loaded trailer) = 6 lbs
You only had 6 lbs available for cargo and passengers in the truck! You are probably about right with that 3000 lbs recommendation, as this will allow for about 500 lbs of passengers and perhaps a cooler in the back.
Good for you on including the diffs in your upgrade. Many people here find themselves in the same boat, and choose to simply trade for a tow-package equipped vehicle. It would help this community if you would post the cost for upgrading to the 3.73 gearing:
1. Front cost
2. Rear cost (for those that only have RWD).
3. Did you recoup any cost for the old parts?
You really need to finish that project for the 7-pin connector. Without it, I assume you are still running without trailer brakes. Your truck's brakes are only rated to handle the trucks GVWR alone (5845 lbs per Edmunds). At 8000 lbs GCVW, you are seriously overloading those brakes.
I'm sure you have trailer brakes on the camper. You just need that wiring, and a good brake controller. I can't recommend enough the Prodigy, P2, or P3, each made by Tekonsha. The each have the same functioning hardware, and the Prodigy and P2 are pretty much identical. The P3 has a more user-friendly LCD display, versus the old-school LED on the Prodigy and P2. But functionally, IIHO, you can't get any better. You can get cheaper time-delay controllers for about $40. But for $89-$140, these accelerometer-based proportional controllers are worth every cent and will give you smoother towing and the shortest stopping distance.
If you already have a 4-flat harness in the rear, you can get a conversion kit from etrailer.com. Plugs into the 4-flat for your lights, but also comes with all wiring and connectors to run the brake and 12V lines up to the engine bay. This is what I used for my minivan, towing a 3000 popup camper:
http://www.etrailer.com/Brake-Controller/etrailer/ETBC7.html