Mazda3Club.com : The Original Mazda3 Forum - Getting rid of low-profile wheels

Preface: I'm a car idiot, really don't know the first thing about how cars, wheels, and tires really work. Please talk down to my level. :)

Recently I bought my wife a slightly used '02 Mazda Protege. The previous owner had tricked it out with a couple of nice sporty additions, one of them being some low-profile tires that lower the vehicle a bit. The factory tires (which I don't have) used to be 185/65R/14 85S, while the tires that are currently on the thing are 205/40 ZR 17 84W. They are Toyo Proxes FZ4's.

We're finding that, while it's a pleasure to drive with these very different-feeling tires (different compared to other similar cars we've had) these tires handle HORRIBLY in rain. And I mean horrible. In our area today we had a lot of rain, and I couldn't go any faster than about 40mph because the car was skidding everywhere and hydroplaning.

Since neither me or my wife are car aficionados, we wouldn't know the first thing about alternatives. All we really care about is safety, and value.
So the major questions are:

(1) Are these low-profile tires generally worse in water? I would have thought they'd be better, but that's just my instinct.
(2) Any inexpensive ideas for solving this problem? I can, of course, buy new tires. Taking a quick look at tirerack.com, I see some budget tires that aren't reviewed very favorably in the $50-$80 range, and plenty of high performance tires for big bucks...which I don't have.
(3) Worth looking at replacing the wheels and going back to a more traditional size where I know I can get good budget tires? (On my very similarly sized Honda Civic, I've bought these awesome Pirelli tires that last forever and control GREAT, and they're cheap -- about $45/tire. But these Pirellis don't come in the low-profile size.)

Any other thoughts...bring em on, I'm all ears. Just make it safe, and make it cheap. I wish I knew people who had a similar car who'd trade with me! (I'm in the Nashville area.) Even though I know these wheels and tires are worth significantly more than the factory tires, if someone was here and offered to swap em out, I wouldn't even ask for compensation! I'd just take the factory wheels!