How to prevent washing machine drain overflow
Well... you've got 22 gallons coming out of the washing machine each cycle. You've got about 2 1/2 gallons in the vertical pipe, and another gallon in the horizontal pipe, so you'd need to store another 20 gallons to be reasonably safe if you go down that route. I wouldn't advise it -- drain water has all sorts of junk in it.

Personally, I've never heard of a floor drain that is 2" or less, so your drain should have sufficient capacity to drain the water thrown off by the washer.

So it sounds like there's some back-pressure causing the water not to flow through the drain pipe as fast as it should. I'd start by snaking it, and if that doesn't work, I'd extend the PVC pipe through the hole and fairly far down the drain; this should reduce the pressure drop and force the water through the drain faster.