Hi,
is this a good idea? What if your IdP is down and you need to perform some administration task, how will you log on? Anyway, I am not sure how you can remove the basic authentication but you could try to use custom login module. It could be setup with higher priority than basic auth. and it could also have failsafe mechanism included to do nothing if some URL parameter is provided. This would then switch back to basic auth.
Cheers