Depends on what platform is used for the conversion, and how heavy the van is when done. A lot of conversions are built on 1/2 ton vans and some are overloaded before you start towing, while others are no heavier than the 12-seat passenger package with dual A/C installed.
An E-350 with V-10 and 4.10 gearing has a GCWR of 18500 pounds. The bare van is close to 6000 pounds (GVWR usually 8800 to 9600 depending on weight options) so that leaves about 2500 for conversion package, passengers, cargo, tongue weight, until you start cutting into the 10,000 pound maximum tow rating, which is basically limited by the frame and hitch.
V-10 with standard gearing cuts you back to 15,000 GVWR, will still leaves you with 9000 maximum tow rating, but now every pound you put into the van cuts into that 9000, starting from empty.
5.4 V-8 puts you at 13,000 GCWR, so that you can tow 7000 pounds with an empty van, or carry something in the neighborhood of 3000 pounds (2800-3600) but not do both at the same time.
Wish you good luck finding a V-10 van, particularly with the 4.10 axle. They were pretty rare, and I don't know that they are making them any more. My dealer told me he couldn't get me one, but I was happy to find the V-8 at a good price.
This is assuming you are looking to find a used cargo van of the right capacity and have a conversion done. Finding a used 1-ton conversion van set up for heavy towing? Chances are slim to none. Most conversions are done on 1/2 ton vans, unless they were built as chair lift vans, then they would use a 3/4 ton or 1-ton to handle the loads from the lift equipment.