The numbers you are looking at are probably "Maximum Tow Capacity" for the original van, at 6400 most likely from a GCWR of about 12,000 pounds. The 1500 on the hitch is probably a rating for the hitch.
What you load in the van (e.g. seven people, their stuff, and everything the upfitter added) further reduces "tow capacity" and tongue weight of the trailer has to fit into what is left of what the van can carry.
The two critical numbers are GVWR (maximum for weight of loaded vehicle) and GCWR (maximum weight of the whole towing combination).
GCWR will be determined by engine, transmission, drive axle size, and axle ratios. With the 5.3 V8 this was usually 12,000 pounds with the standard 3.42 axle for the Express 1500 series, 13,000 pounds with standard 3.73 axle for Express 2500/3500 vans. Axle options might change this (i.e the 3.73 option for 5.3 V8 on Express 1500 gets you 13,000 GCWR).
GVWR is determined primarily by suspension components (including wheels and tires) and was in the range of 6200 to 7300 pounds for Express 1500, with the 7300 rating most often used by conversion van upfitters. Express 2500 and 3500 in that era got 8600 and 9600 pound GVWR, respectively, as their highest ratings.
So what you can do will depend in whether your van was built on Express 1500, 2500, or 3500 (the later most unlikely for a passenger conversion). You need to know those two numbers, GCWR and GVWR, then weigh your van with the all the people and stuff it is going to carry. Actual tow capacity will be GCWR - weight of loaded van. Maximum tongue weight will be GVWR - actual weight of loaded van.
Example of where I am with my 2102 E-350 wagon. GVWR 9500 pounds, GCWR 13,000 with 5.4 V8 and 3.73 axle. "Maximum Tow Rating" is listed 6700 pounds, assuming empty van weighs 6300 with full fuel and driver. Thus alone with no load, I can pull a 6700 pound trailer and have 3000+ pounds of carrying capacity to handle whatever the tongue weight.
If I load up with my daughter, her husband, two granddaughters, and the 300 pounds of luggage they'll bring with them, and another 100 pounds of camping gear, my loaded weight goes up about 7300 pounds, so my remaining towing capacity is down to 5700 pounds, and I'm down to 2200 pounds of load capacity to handle tongue weight.
If I load both daughters and their families (eight persons) with luggage, my load goes up to about 1600 pounds, for a loaded weight of 7900 pounds, my towing capacity is now down to 5100 pounds, and have 1600 pounds of load capacity to handle tongue weight.
But if this was a lighter E-150 wagon of earlier vintage, with 7300 GVWR, 12,000 GCWR and 5500 empty weight, empty towing capacity is 6500 and I have 1800 pounds capacity to handle tongue weight. With my smaller family load bringing loaded weight up to 6500 pounds, towing capacity down to 5500, and I would have 800 pounds to deal with tongue weight. With my larger family load, loaded weight goes up to 7100, towing capacity down to 4900, and I have only 200 pounds left for tongue weight. Working out these numbers is why I passed on buying an 8 passenger E-150 and got a 12 passenger E-350 (and took out that 200 pound rear seat).
My hypothetical E-150 case is likely close to your situation, making it so important to know exactly where you are on weights and ratings. If your conversion is on an Express 1500, you may be marginal for carrying capacity to handle the tongue weight, and with your van loaded the remaining towing capacity has probably melted down to about 5000 pounds, or a little less. Not much less, or your van would be overloaded. If it was built on Express 2500 with the 5.3 V8, your towing capacity loaded is still probably close to 5000, but you are less likely to be close to max weight for the van itself.
Your best tow vehicle option for a family that size today is the Express 3500 passenger van, with 6.0 V8, which will have 15,000 or 16,000 GCWR (depending on model year/transmission) and 9500-9600 GWVR. This comes in 12 and 15 passenger versions, and the rear seat is easy to remove for 8 or 11 passenger capacity and lots of luggage space. Loaded to 8500 pounds you would still be good for 7500 pounds of trailer. Not as nice as a conversion van maybe, but rated for 200 pounds of passenger in each seat position.
Prices will depend on age and mileage; early 2013 they were about $20K for a year-old van coming out of rental service with 20-30,000 miles, they've gone up since because discontinuation of the E-series made used vans with V8 engines a lot more precious.
