Interesting scenario. With my previous TT I used to bottom out the hitch all the time, but now with a longer TT that sits higher above the axle, I rarely have that issue any more. My subdivision was built with all sloping face curbs, and most driveway have a significant lip/bump to get over. I am fortunate because it is obvious that the previous owner of my house ripped out the sloping curb across the mouth of the driveway and replaced it with a much flatter one in order to eliminate the problem. Several neighbors have the old sloping curb across their driveways, making it difficult even to drive regular cars over it.
I wonder if you could build something by layering lightweight plastic lumber that conforms to the gutter area and provides a easier grade into the driveway from the street. These plastic lumber products are pretty much indestructible and won't rot or splinter over time. I've used it extensively on my backyard decks. You can buy them at Home Depot or Lowes. They are more expensive than conventional wood, but you shouldn't need large quantities.
Another option might be a product I also used on my decks. It is a thick rubber patio tile. You could cut a few to length as needed to fill the gutter area. You can see them here on Home Depot website:
http://www.homedepot.com/p/Envirotile-Bella-Rocca-18-in-x-18-in-Terra-Cotta-Paver-4-Case-MT5000808/203062136