The "rated" cargo capacity for my Ranger is about 1,100Lbs. I routinely haul 1500-1600Lbs of scrap in it. I have "accidentally" put 2,000lbs in it once or twice, and it definitely didn't feel quite right. I've also replaced EVERY suspension and steering component, including heavier leaf springs, with rear "overload" shocks.
The Explorer is going to have a lower cargo capacity, because you're already carrying around the weight of the rear body. Granted, the Explorer has a slightly "beefier" rear axle, but everything else is the same as the Ranger (motor, trans,etc...). I wouldn't try more then 1,000lbs in the Explorer, if that.
Why not make 3, or more, trips? I'm sure you're Explorer (or even just the transmission) is worth more then the cost of a little extra time and gas. If you are picking this stuff up at a Lowes or Home Depot, you can rent one of their trucks for somewhere around 20 bucks.