You could pick up a $100 6.5HP Predator 212 cc Harbor Freight special assuming your Tecumseh is a single shaft engine. That might be the easiest fix. Currently $149.99 and often on sale for $99.99 - $129.99. If you look around you can usually find coupons too. Going to have to decide how long you are willing to wait vs how bad you need the blower. Luckily no one seems to be getting any snow this year.
http://www.harborfreight.com/engines...nia-68120.html
As for your actual engine. I have heard of valve problems on the smaller 3.5 - 5HP Tecumsehs so maybe you just need yours redone. Most valve issues end up being clearance issues and when they heat up the valves don't fully close and the engine looses power and eventually stalls from lack of compression. This doesn't seize it though, it simple turns over too easy. I am afraid you are going to have to start tearing things apart and hope to find the problem.
You said it has plenty of oil, but you didn't say when it was last changed. Also, if your carb has been leaking all that oil you have could actually be gas instead. Very dirty oil and lots of gas in the oil can be about as bad as no oil at all.
You did mention overheating. Another thing to check is remove the back recoil cover and make sure there are no animal nests in there. Animals like to build nests in the fins on small engines and that blocks the cooling and causes heat buildup problems. If that is your problem you might get lucky and it might run again at least for a little while after it cools down. Just make sure to clean all the fins before running it again.
I would start with the simple things like removing the belt cover and removing both belts. That will tell you if the problem is the engine or the blower.