Somebody mentioned that your reach might be too long, and that's what I'm kinda thinkin' too. Sounds like your pelvis is trying to move forward or collapsing forward, and tilting the saddle is supporting it and forcing it back.
A new saddle (especially one that fits) will likely make a lot of difference, but I'd also look into bike fit and core strength. Your reach might be too long for your structure or too long for your core to support.
(now you have a gazillion things to check, don't you feel reassured? )
"If Americans want to live the American Dream, they should go to Denmark." - Richard Wilkinson