In the hope that new available datasets will be of help to others who are looking to achieve these results, here's my two cents:
To the question "Is there a way to create a relatively precise topographical map of a private land using GPS elevation data?", I fear the practical answer is no and will never change to yes especially if it's a heavily forested area. There is an alternative though.
Since I am pretty sure the OP is from Québec, it might be of interest to know that the government is in the process of rolling out lidar coverage for the southern parts of the province. You can check out if your area is already covered here:
overview of lidar campaigns and available tiles
If not, you'll have to wait a year or two or wait until 2022 or 2023 when the last campaigns will conclude.
These datasets are very precise, at a spatial resolution of 1m (each pixel has 1m sides) and the vertical accuracy is under 30cm. You can build contour lines at 1m interval with confidence.
This of course also applies to any other area with similar coverage, making consumer grade GPS survey pretty much useless.