I finally managed to reduce the size of the doxygen docs to around 500Mb, and make their appearance integrated to the rest of our web stuff, so I'm uploading it now to http://www.freecadweb.org/api/
The uploading is not finished, will take a couple of hours
but the main pages work already.
There is still a lot of work needed on these docs to make things clearer, better group members under structures and namespaces (specially on the python side, where namespaces are automatically taken from filenames, which is not always meaningful). Nevertheless, I think these docs already do a better job than the old sphynx ones.
When building the docs, there are now two make targets: "make DevDoc", which is the original one, which is unchanged, and "make WebDoc", which produces this stripped-down version. Basically it doesn't build the graphviz schemas, which takes almost 1Gb, and it doesn't include the header files. But I managed to have the doc page include a link to the respective header and cpp files on github.
The doc will need to be rebuilt and uploaded manually from time to time, (unless one of you buildbot wizards manages to do that automatically) but it's easy enough.