Well there's your easy way out of finishing the production. Call the Fire Marshall and report unsafe conditions. Boom. Closed show!
Wet floors are no excuse to not retape. If you have blood clean up daily (by the way....your show sounds like a real pick me up!) mop at night, leave it overnight to dry and retape the cable in the evening at show call. If the director requires you to mop preshow, there are other tapes that work in wet environments that can keep the cable down like Vinyl/Dance floor tapes. The onstage issues and safety really falls under your role as stage manager and not a designer or producer. They may have made the mess, but it's up to you to make sure your cast in safe.
I don't mean to sound harsh but when it comes to safety after a certain point it's no longer a producer/designer issue and someone has to take control and do what needs to be done.