Is $11,200 to build a concrete surface trench drain a fair price?

My 1890s home was built with a 12-inch setback from the neighbor's property, which slopes directly into ours. This causes a lot of heaving in the soil. I spoke to two landscaping companies with different approaches to solving the problem, and I'm trying to determine which is the more ideal solution. The proposal two guy said concrete would eventually fall apart and is too expensive, while the other folks said a French drain needs to be installed further from the home. We have a crawl space, but I haven't seen water down there during rain. I plan to install water meters. The main problem is the heaving, which causes doors to be sticky and require continuous adjustment. A structural engineer's report indicated that the floors are approximately 1.7 inches out of level at the newer west side and 3.7 inches out of level at the original east side, which is significantly more than the typical 1.0 inch for a home of this age. Some foundation walls were also found to be 2-2.5 degrees out of plumb, compared to a typical 1 degree. Although the foundation is from the 1890s, the home was entirely rebuilt (except for one wall) just 2-5 years ago. My primary goal is to prevent the doors from sticking, and while cost is not prohibitively high, I want the best possible solution.