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.
Give big space to the festive dog that make sport in the roadway. Avoid entanglement with your wheel spoke.
(Sign in Japan)
1978 Raleigh Gran Prix
2003 EZ Sport AX