With a bit of mucking about Strava can use the data from a GPS with barometric altimeter, even if it is not one of their listed devices, which are the Edge Series.
Their API for
developers explains that if the creator tag is changed it will use the elevation data from the GPS. So, to quote the relevant bit from their page:
A generic “with barometer” device is provided to force the system to use the elevation data from TCX and GPX file types. One only needs to add “with barometer” to the end of the creator name. For example, a TCX file would include something like:
<Creator> <Name>My Awesome App with barometer</Name> </Creator>
and a GPX file should have an updated creator like:
<gpx version="1.1" creator="Best app ever with Barometer">.
Use a text editor, open file, add "with barometer", save and upload as normal.