I think you'd find such a change counterproductive. Such a license would not qualify as OSS anymore, which would take away the vast majority of the value. So, you'd incur all the costs of releasing the source, without getting the value of OSS.
You might consider something like the AGPL instead, which still qualifies as Open Source, but which provides added protections for a hosted service.
Wouldn't AGPL be moving is basically the opposite direction from what cookiecaper was suggesting?
(I'd also think AGPL would be less OSS-like than that suggestion, since it limits what changes you're allowed to make instead of just limiting how you're allowed to distribute it.)
It would not qualify as OSS as defined by political figureheads like Stallman, Raymond, et al, but if I can access the code, make changes, and share the changes with others, it's good enough for me.
As another commenter pointed out, AGPL is actually the opposite direction, as it merely applies the copyleft constraints of the GPL to hosted software.
You might consider something like the AGPL instead, which still qualifies as Open Source, but which provides added protections for a hosted service.