So I haven't yet ridden a century on my vintage bike but I have ridden many many centuries on just about everything else I own. Fwiw, I totally planned a century on the vintage but it got cancelled due to covid, familiar story.
Anyway, it's legs, butt, and back. For me, upper back but for others, lower.
Legs - most people have 50+ in them today if they had to. Like life or death. The key is getting enough distance to enjoy the miles and to still feel ok after mile 70. I think you're doing ok here.
Butt - three parts. 1. a saddle that is shaped properly for you. 2. Adjusting the position of said saddle to make it comfortable 3. Time on the seat to harden the butt. In general, this pretty much comes with training your legs. For vintage, I could see a problem if your ideal saddle just hurts. I know he'll would have to freeze over before I'd switch mine, even if it hurt. However, my vintage bike isn't my big day bike.
Back. Kinda like the saddle. You've got to get the fit right. This is stem length, height, and handlebar width. On a vintage bike, the "hoods" riding position isn't as easy so you'll need to tinker. Of course seat height matters here too. Also, make sure you can ride hands free long enough to stretch and eat. Those throbbing muscles don't get better if you stay in the exact same position for 5-8 hours.
Other than that, just make sure you can carry enough water or have support. Choose a route that compliments the gearing on your bike. I know with UG on mine, I'd have to change more than I'm willing to if I wanted to make it a mountain goat.