They sell pedestals to raise front loaders 12 to 15 inches off the floor, but they're kind of expensive. Every manufacturer makes one that matches the contours of the appliance. Unfortunately, I don't think they're worth half the money they ask for them (those pedestals are sometimes a $200+ add on--$400+ for a pair!--for what is essentially a hollow steel box). I'd think you could build something out of 2x4's and plywood (and paint to make it look nice) for a lot less. If you're extra creative, you could even build in storage drawers, just like the ready-made ones have. (Maybe it's not the greatest idea for you guys... I'm just thinking on the fly...)
The thing I've noticed about front loaders is that while basic ones start in the $600 range, you'll really pay if you want the larger capacity models. OTOH, even a smaller front loader has as much usable capacity as a larger top loader because there's no agitator taking up room in there. Also, because a front loader works by sloshing water through the clothes, rather than sloshing the clothes through the water, you can probably stuff the machine a little tighter than a top loader and still get good results.
Yet another thought... Your usable capacity per wash load will also be limited by the size of the existing dryer if you don't replace it (assuming that you usually dry everything in the dryer).
According to the Consumer Reports reliability survey, Whirlpool, LG, and Kenmore are the winners amongst the popular brands of front loaders, with Maytag giving a surprisingly poor performance.
For top loaders, the winers are Roper, Frigidaire, GE, Whirlpool, and Kenmore, in that order. (Roper is a very low-end brand, so with few extra features that can break down, that result is not so surprising.) Amana is the big loser on the CR chart, but Maytag and the high-end Fisher & Paykel brand are barely any better.
BTW, I hope your grandmother will be OK. It sucks when the people you love get sick. (My step-mom is battling cancer right now--it's rough thinking about it.)