I just switched from an aluminum frame to a madone. I've also had back problems in the past. One thing I noticed is, the carbon seems to transfer less road vibration to my body. I just rode 43 miles without any back ache. Try one of the cheaper madones, if you're on a budget. The 4.7 is consideraby cheaper, but has lower end components. There is also a $200 end of season sale, if you can find your frame size.
Don't focus on the pain while riding. Try doing a few stretches while pedalling, or stop on the side of the road.
"Well-behaved women seldom make history." --Laurel Thatcher Ulrich
'09 Trek WSD 2.1 with a Brooks B-68 saddle
'11 Trek WSD Madone 5.2 with Brooks B-17