I think your bike is fine as well. Like many have said nothing wrong with getting a new bike if that is what you want.

To build endurance you must simply (or not so simply) push past the point you are right now. Part of it is physical and part of it is mental. The physical part is you simply need to ride more. 1350 miles is great don't get me wrong but you need to invest more saddle time. Work up to your fitness. Go on some shorter rides but at higher intensity. If you are giving out at 40 plan a 45 but go at it slower. Make sure to fuel and hydrate properly. And just as important as the preparation physically prepare yourself mental. Convince yourself I have done the training there is no question it is possible and there is no question I will succeed. Then go out and do it. Train on shorter higher intensity rides for a couple of weeks then go out and do 55. Rinse repeat go for 62. Getting in a group instead of going it alone is a huge help as well

There is a ride we do with 5th graders and take them on a 7 day tour the longest day is 55 miles. Everybody succeeds. How? there is a set plan for training certain mileage and hilly or even mountains routes must be completed. But more important is the factor of installing the belief in these young riders. Before they take the first pedal stroke on the tour they believe they can do it. The support group around them is also key.

I think you are more than 3/4 of the way there now. You have a good bike, you have miles under your belt, you have the desire. You need to push past a couple of barriers and you will be a century rider with ease.

Good luck