Here's what the Alberta Parks website says about boats: Boats used on any water body must
conform with the Canada Shipping Act and regulations. To obtain information on boating regulations and general boating safety contact Transport Canada at 1–800-267-6687 or visit Transport Canada’s marine transportation web site at tc.gc.ca/eng/marine-menu.htm.
Doubt you'll get any traction with Parks Canada. Minnewanka is likely not an option. They fought hard enough to keep the airstrip closed.
Your side note is really where your answer lies. It's impractical. You might be able to land on Spray Lakes, but where will you beach or otherwise secure it. It will be at risk of hail damage in the summer. We get a lot of hail here.
I really like amphibs. I take my airplane out of the hangar and splash around in local lakes, or take it somewhere that I don't fear hail damage. I taxi up to the pumps and fuel up instead of carting gas cans to a shore line somewhere. I can depart a lake at dusk and fly home to a night landing. On the flip side, it's heavy, has all the performance of a 172, and twice the fuel burn. It's also slow and inefficient. 120 knots at 17 GPH IS 7 nautical /gallon.
I sure wouldn't leave it unattended in a provincial park, subject to wind, hail, theft, and vandalism!
Buy a cheap car and leave it at Springbank for use when you're here. It'll be cheaper and less risky. Fly from Saskatoon on wheels, jump in the car, and your total trip time will still be less than flying to Spray on floats, just not near the glory!