The cheapest thing is to extend the wires to a new location.
You could also look at a water leak detection system (like the Water Cop) that would detect a leak and automatically shut off the main water to the house. This would prevent major damage from occuring, but just the automatic water shut off valve runs several hundred dollars. So the total cost of a sytem is going to run at least that amount.
The advantage to that system is that you could feel comfortable with electronic equipment located on the floor below the washing machine, and you could extend the system to protect the entire house from leaks by placing sensors under each fixture. Don't forget about the dishwasher and any ice makers (even those in freeezers). One detected leak could save your butt and be well worth the cost of the initial installation of the system.
I'm leaning towards moving the closet at this time, that will give me more room for the bathroom down there

(2 1/2 baths currently but there kind of small I think a large bathroom down there would add alot of value to the property)
like the idea of using moisture sensors to detect leaks, I have a well so it might be easier to just kill power to the pump when moisture is detected. but in the event of the drainage hose from the washing machine coming loose I'd have to kill the power to that as well.
fortunately I've been to lazy to terminate the mini coax, trying to figure out the cost per foot of that cable and compare that to the cost of connectors to extend it. Might be cheaper to rerun those. I don't think I'd run into any problems extending the rg6 and cat5.