It's hard to tell if the camera is distorting the slope.
24" in 20' would be a 10% cross slope. From the picture, I don't think you are quite that bad. Easy way to check is to take a level set it roughly where the trailer axles would sit on the ground and then with a tape measure lift the downhill side until the bubble shows level. Divide the height (in feet) by the length of the level (in feet). That will give you the actual percentage cross slope where the axles will sit. I wouldn't be surprised if you find it only 5-6% but again, it's hard to tell from the picture.
If it's only 5-6% 2-3 boards should get you pretty close to level with putting it up so high you are worried about it falling off.
Someone else mentioned backing it up until the wheels are off the pavement. I know you mentioned the cost of having that done but assuming you have a pickup, you could go down and get a load of gravel and do it yourself in an hour or two. That would get you by until you can have the pavement extended. I haven't priced up gravel lately but should be under $100.