The use of snow thrower tires on brush cutters is not unusual. DR, Swisher, Agri-Fab all use them. The can't just buy the tire is not unusual in today's replacement of complete module instead of just a single component, IE, have to purchase an entire air filter assembly to get the air filter or have to replace an entire engine blower housing to get a starter rewind spring . And they did honor their warranty up to the point that it states in the actual warranty page in your owners manual that unauthorized alterations will void the warranty. Unfortunately your use of the aftermarket belt voided the warranty. Maybe a little nitpicking but within the warranty guidelines.
The vines catching under the mower is common on that style of mower not brand dependent It will hook under the edge of the mower with or without feet and drag it off line, or in some cases will try to climb up the vine. And the skirting is more designed for tall weed and grass clipping not brush mowing, and while cutting brush I can see the skirts getting ripped off shortly. Not a good design, but more of a meet safety guidelines than function scenario.