Hi Tarababe,
I have a similar issue with my gunmetal bayswater made in soft tumbled leather. This poor bag believes itself to be a puddle at every possible opportunity and as you rightly point out a baseshaper does very little for these spineless members of our bag collections.
To try to resolve the issue I've comissioned the long suffering Johnny to create a base with spinal board......it is still in the prototype stage, so I'll keep you posted on design progress.
In the meanwhile, the only other thing to try would be a bag organiser....there are several manufacturers out there including Tintamar, and these from an Etsy seller...
http://www.etsy.com/shop/samorga