I RIDE A 2005 SPEEDMASTER - I have had a bad back for 45 years and I'm on my second back operation(now have pins and pedical screws in L4,L5 and S1). I have put 23,500 miles commuting 41 miles a day and have taken 500 mile per day trips. I ride a minimal pad custom seat you can purchase through Brent at New Bonneville.com and have never hurt my back while riding. I do hurt my back as you describe at least a few times or more per year.
I think The America and Speedmaster sit and ride pretty much the same.
I don't think the bike will be to blame if your back hurts. It is very useful to keep your stomach muscles in shape which I think is essential in protecting your back.
Best of luck and tell the dealer you will need at least a 30 minute ride to make a decision.
Gary