Forgetting for a moment the issue of "would a new bike be faster," which has consumed way too much of this thread, I would offer some advice:
Been there, done that, though when I was only 50. I got it into my head that I would do the one-day STP, so I bought a $100 used 10-speed 27" Nishiki that probably weighed 30 lbs. and went at it. I was an avid hiker, so this isn't quite as crazy as it sounds. However, total failure. I started riding in early spring. The first time I tried a solo century, I wound up sitting in a ditch at 75 miles, bonked and crying. So I gave it up for that year. Good idea.
That winter, I traded up to a $250 used 12 speed 27" bike that weighed 27 lbs. I bought a set of rollers. I already had a heart rate monitor from the Summer of Failure. I put SPD pedals on the bike and bought a cheap pair of MTB shoes. I already had the clothes, etc. I bought Friel's Cyclist's Training Bible, read it cover to cover, and built year-long training plan. I trained all winter on the bike on the rollers, lifted weights at the gym, and rode outside whenever the weather was decent. By early spring, I was averaging 15 mph on easy 60 mile rides. In June, I did a hilly 200k group ride and met 2 women on it who taught me to ride in groups, pace myself, pull, draft, signal, and all that. We teamed up and I rode the STP double in July, no problem other than I had to pull them for the last 120 miles to Portland. Took me frigging forever out in the wind on that tank.
So that was my program and I recommend it to the OP. Forget it this year. Learn to train. Learn to ride. There's a lot more to it than pedaling. Put 5 mph on your average. It is the motor. You'll have a lot more fun and less failure if you train to ride strong. Just put in the miles.