Can this be solved by storing a timestamp of the record along with precise GPS coordinates? Could we then utilize some database to compute the drift from then and now?
Yes, in fact it should essentially be mandatory because the spatial reference system for GPS is not fixed to a point on Earth. This has become a major issue for old geospatial data sets in the US where no one remembered to record when the coordinates were collected.
To correct for these cases you need to be able to separately attribute drift vectors due to the spatial reference system, plate tectonics, and other geophysical phenomena. Without a timestamp that allows you to precisely subtract out the spatial reference system drift vector, the magnitude of the uncertainty is quite large.
You don’t need to store a timestamp, but the local coordinate reference system that the coordinates are in. When revisions like this are made, it’s by updating the specification of a specific local coordinate reference.
WGS84 is global, but for most precise local work more specific national coords are used instead.
I mean, certainly - if you store both GPS time and derived coordinates from the same sampling, then you can always later interpret it as needed - whether relative to legal or geographical boundaries etc as you might want to interpret in the future.