Planning a HIM and a century ride?

I don't have specific advice on timing, but that ride looks crazy! I've only done the App Gap (from the opposite direction) and the views are awesome, but it's definitely steep. Are you planning on doing Timberman? That's relatively hilly. Perhaps you could plan to do the VT ride as your last long ride before your taper. Then you'd definitely have some solid hill work in prior to the HIM, but ideally be completely recovered by race day too. You could also just plan it for the fall once you've recovered after the HIM.

I'm planning on doing the B2VT (formerly Harpoon B2B) ride one week after doing Eagleman, but that's just due to unfortunate timing. I wouldn't necessarily recommend a schedule like that!

I did something very similar 2 years ago. HIM in early July, and a 150mi/10k ft ride about 2.5 weeks later. I was fine to finish the long ride, wasn't by any means my fastest riding ever, but I didn't have a hard time finishing. Depending on your goals I would say 2 weeks min of rest between the two is enough to finish.

I would look at some point in June or early July. Gives you time to get good base on the bike, then after the century you can start focusing on speed.