Are you saying the washing machine has to pump the water up to a drain six feet above the floor? This is an absolute no-no.

Even if it pumped for the whole duration of the spin, as soon as the pump stopped at the end, the whole drain hose full of water will gravity-drain back into the machine. If there is no air break at that point, it may even siphon water back from your drain.

The owners manual will have specs, or possibly a diagram, showing the max height of the drain, it will be probably less than four feet. There must be an air break at that point to prevent siphoning.

If the installation is what I think you are saying, you will have to change the installation. Either move the machine to a better location, or install a tub or sump for the machine to empty into, with a greywater pump controlled by a float switch to elevate the drained water to your drain.

I'd be wary about trusting a check valve.

Washing machines pump out muck, lint and bits of stuff in the water, this is likely to get caught in the flap and either cause it to leak back, or to block up over time.

The Filter Flo was a creature from a different era. They had a very strong pump driven by the main wash motor, current machines use a tiny magnetic motor inside the pump, it only  consumes 10 watts or so. Also the Filter Flo was known as a water hog - huge clearance between the inner and outer drums, so any bit of back flow would have been an insignificant puddle in the base of the outer drum. A modern front loader is designed to minimize water use, this includes tight clearances between drums so a bit of backflow is likely to re-wet the washing.

I'd be inclined to fit a non-return valve as a first trial. Preferably one that uses a ball inside, less likely to gum up than a flap valve. If that makes the problem go away, I'd look at a long term solution of draining to a tub with a grey water pump in the base.

(a sump pump?) Or.... drain the water into the old Filter Flo and use it to pump the water uphill...