So the thing is, if you get a visa from any Schengen country, you can freely cross borders within the schengen area.
You can get a schengen visa from any EU country which is part of this agreement. The visa itself will be sticked inside to your Rtd. it doesnt matter if you have pr card or not. Actually its easier because when you come back to Canada, you dont need to present you pr card to cbsa officer (but you have to go through immigration every time you come back, which is usually a longer line).
I know its tough to get a schengen visa, thats why a lot of people wait until they become a citizen, or they may find other ways. Other ways means they travel to italy, and they can visit other EU countries from there. They do this because actually the land borders are open, and they wont stop you if you travel by car. But I dont recomennd, its risky, and maybe sometimes police can stop you, and you have to show ID’s or passport. And if you dont have the schengen visa, you may have to pay a fine. Dont risk it. Some people on this forum wrote they had a european road trip, without visa..
if you’re not in a hurry, definitely try to get an appointment, but it will be 6+ months.