I'm a firm believer in N+1, but no getting a carbon bike will not instantly make you faster or let you ride longer.

If your training plan is to simply ride lots and 'push a little harder each time,' then you probably have no idea what's required to get faster. Which is fine if you just want to ride for enjoyment. If you want to get faster, get a HRM and a book on how to use it. Then develop a training plan. Your current method is not a plan.