Think something involving the words goal (with either a soccer/hockey goal or basketball hoop - whatever is popular in your school or area) to get the pun for gym and sports.
Have you thought of a fundraiser just for the floor? Pledge drive, walk-a-thon, adopt a plank (paint a section of wall in the gym and put up a frame with the list of donor names) obviously away from where it might get hit by balls or something but something to acknowledge people for their donations. Purchase a plank, support a sander, and volunteer for varnish. I'm just guessing those are some things that go into a new gym floor but you get the idea. Work out the cost of the floor (get a solid estimate plus extra) and then divide out how many planks (cost per plank), how many hours of sanding, and how many containers of varnish. As long is it's close to what someone might find in Home Depot or Menards (like a gallon of varnish = $$ and we need XX gallons)
On your original idea - I like the idea of 4 for the floor but if you are already having trouble with participation, that might wear off by the end of the school year. If the events/fundraisers aren't at a good time, or aren't something they wish to buy, the families will probably just blow off the pledge to participate since they aren't real into it in the first place. I know that's how it was at our last school - super frustrating for all of us who cared! But hey - any way you can get more people to participate and get that new floor for the kids is a good thing!!!
Kicks for kids? Can you tell I'm just thinking out loud here?
Good luck!!!