Recumbent rider here.

"They" say it takes about 1-3K miles to really feel one with a recumbent, so the weird feeling is natural. I loved mine right from the start, but was a bit wobbly at first.

It wasn't my back that put me on a 'bent, it was my wrists. I have very bad conformation there - prone to arthritis, carpal tunnel, and just general pain. I just couldn't see riding the long (slow) distances I love on an upright. Not an option for me.

I haven't done a century (yet), but did ride RAGBRAI this year. DH & I were the couple on the matching blue 'bents. The day with the optional century on RAGBRAI was the day that I was really struggling, so it was a Good Thing I kept my mileage to the "smaller" 70 or so that day. On a good day it would have been a stretch for this fat old broad, but I could have done it.

And for that matter, RAAM (3000-ish mile across America in a week or so) often has 'bent teams that do Very Well.

I love my 'bent. I hope you'll enjoy yours.