I'd suggest adding a sports med PT or a PT who also does bike fit into the mix.
In all likelihood, your posture on the bike is off more than your bike fit is off.
A bike fitter can make sure your bike is set up correctly, but sometimes it takes a PT or fitter with PT-type background to be sure your body is set up correctly!
(and climbing stairs has the lumbar spine sustained in a very different degree of flexion than sitting on a bike, so I'm not at all surprised you can climb stairs fine.)
"If Americans want to live the American Dream, they should go to Denmark." - Richard Wilkinson