I live in the Minneapolis area and just put a set of Continental True Contacts and my size is 225/65 17. I LOVE Continentals. It's the only tire brand I will buy. I worked in the tire biz for 4 years when I was just out of high school, and raced cars is local autocross, and had a hobby Audi repair shop for years. So I have some idea on tires. First off, 31 PSI on a tire that has a top PSI rating of 51. I don't like how the tires handle with that low of PSI. 33 PSI that is on door beam is too low I think. Every car I have driven handles badly when put to the OEM side beam PSI. I run 40-42 PSI in front and 36-37 PSI in the rear and test this after driving around 5 miles in summer and 10 miles in winter. I go with 40 in the rear when towing because I u sally have a loaded area behind the back seat and trailer tongue weight added.
TrueContact - 225/65R17 102T Tire | Continental
I the old OEM Bridgstones off at 26,000 miles and they were at 4/32 and sold those for $125 and put that in for the new set of True Contacts. Add the $100 from Discount Tire and $70 from Continental, I only payed $100 for the new set. I myself like Continental's Traction Grooves technology, as seen in this video below The True Contacts have that technology and the DWS rating system which is a name of one of their Ultra All-Seasons but is it also stands for Dry/Wet/Snow and the letters are casted into the rubber on the tread to show when the S wears away it is suggested it is not good for snow anymore and when the W gets wore away it is not good for Wet anymore.
That being said, your tires are rated for 50,000 miles and got 37,000 out of them. That's good, you never get the manufacture set amount. Some do, most don't. You even said they are almost bald. No tire will do good in that condition. You look at all top brands , even Michelin people complain on noise, ride, and wet/snow holding ability when any tire gets under 5/32. I pull my tire at around 5/32 to 4/32 and i sell them on Craigslist to people that will be glad they could get tires at a cheap cost with some tread left on it. Then you don't have to pay for junking your tires. I only expect to see at best 35,000 out of the True Contacts before selling them again to get new. My wife has a heavy foot and is hard on the brakes, so tire life is reduced. I just don't like bald tires in Minnesota winters for my wife, AWD or not. I will do it again on Discount Tires 4th of July sale, it seems to be their best sale time. I even waited 1 month to put them on and let them store them, because they don't carry that size and had to get them. It was not even on their site. I just shopped to see the sizes on Continental's US site. Which believe it or not is always accurate on what sizes available. The next time around I may have to buy them on the 4th July sale and take them home till I get the wear at 4/32 that could come early or mid spring or late fall.
Have you had your Rav4 in for a 4 wheel alignment and reset for maximum mileage for tires and NOT just in the broad spectrum swings that are considered "in spec". Example: My Hyundai Elantra GT is all squarely in the rear when on icy snow because the rear alignment is way out but "still in spec", way on the end but Hyundai won't do it under warranty. SO if I decide to keep that car I will have it re aligned at a racing specialty shop so I know it is done right without the attitude "it's good enough."
Here are the tires I have on my Hyundai Elantra GT. Sold the OEM's with 15,000 on them and sold them for $225. I bought 2 sets on DT 4th of July sale. The second link below here is what I had on my Honda Fit that I just sold. Notice the nice tread patterns Continental has, all these tire I posted had the DWS and Traction Groove Technology. It helps.