We learn something new every day :-)

Thanks to this, I have now discovered that rsync treats all --exclude
paths as relative to the source directory, so the exclude you've used -
which I would have fully expected to work - actually translates in rsync
as '/home/home/mike/.gvfs'.

Try

sudo rsync -azvv -e ssh --exclude 'mike/.gvfs' /home/
mike@...:mike_laptop_home

and see how that works.

And thank you for teaching me something new