@ensign has done some work with a moving/drifting sensor stations: https://www.fondriest.com/news/hydrosphere-drifter-brings-lagrangian-sampling-freshwater.htm
The way Monitor My Watershed’s data portal is set up right now is very “site-centric” – the web pages are just not set up to accept moving sensor data like you would generate. The database model which the website is built on can manage trajectory data, but the portal isn’t exposing that portion of the database. To put the data in right now you could pretend it’s all from a single station and then call latitude and longitude two of the your measured variables, but that’s definitely a cludgey way to do it.
For how the trajectory results can work in ODM2, see: https://github.com/ODM2/ODM2/blob/master/doc/ODM2Docs/ext_results_measurementframeworks.md and https://github.com/ODM2/ODM2/blob/master/doc/ODM2Docs/ext_results_trajectory.md