As a general rule, I don't make major decisions on a "what if".
However, it's a 5 year old Hyundai, with high miles and known engine issues, and we do know that even frequent synthetic oil changes won't eliminate the problem of blown Hyundai engines. Let's not forget the other upcoming maintenance issues older, high mile cars have. Note: The Corolla is known for carboned up pistons/rings and oil consumption. In a Corolla, the use of synthetic and frequent oil changes solves the issue.
So, let's look at it another way. Cost per mile. Fuel, capital cost, insurance, maintenance and consumables and your car's resale value. I very much prefer NOT to have to deal with major maintenance issues, as they have hidden costs too, such as rental cars, miles on another vehicle, and the very real risk of poor quality work. The cost per mile is never more than 5c per mile different whether you keep an old vehicle or purchase a similar vehicle brand new when on sale. People concentrate on capital costs, ignoring the fact that the other costs outstrip the cost of a vehicle. Please, do an accurate cost per mile comparison, include the selling price of your current car.
You may find that a well chosen new car won't cost you significantly more per mile, and will be covered by warranty.
In some states, the sales tax is also deductible.