To tow or not to tow or can my van really tow

Hey everyone,
I am new to the forum and I just purchased a used wells cargo trailer. My van is a 2001 GMC Savana 3500 LWB cargo van with the 5.7L Vortec and I believe a 4 speed transmission. The original owner states that the trailer has a gvw of around 7500 pounds and towed it with his Ford Econoline 350. Well the other day I loaded her up with about 3000 lbs and could barely get the vehicle speed over 35 MPH on the highway and pulling hills felt like I was going to blow out the tranny (engine roaring and barely gaining speed). The van was pretty much empty except for me, a passenger and a tool box. I figure the curb weight of the trailer is 2500 and together with the 3k load was around 5500 lbs gross weight.

I have hauled a few HEAVY loads in the van, upward of 2500 lbs, and that feels very heavy. Normally I move around 1000 lbs on average.

Right now I am under the assumption my van simply can't handle the trailer and I have to buy another van that is spec'd for towing. And buying a new or even used van is out of my budget. Is there anything I can do to increase my vans towing capacity? I know the rear ratio might be a problem, I am looking into finding out what my ratio is.