Another option is to replace the pickup bed with a flatbed or hauler style bed. Then you don't have bed rail height or tailgate height to contend with and can level the trailer without raising it.
Many folks around my rural area put flatbeds on their new pickups. It's very popular with the horse/rancher types out here. Most pull large gooseneck horse/stock trailers with living quarters.
Here's a nice aluminum flatbed with built in storage boxes on a Dodge 3500 dually. The bed is by Bradford-Built, a popular brand around here.