We did a little research on this one and are convinced that we somehow know less now then we did in the beginning. It seems water can make things much worse (surprise !) and organic materials (such as the cotton upholstery on your Olive Bantam) are more delicate and therefore more challenging to clean than synthetics (not such a surprise!). Therefore, we'd most likely go with a pro upholstery dry cleaning and after a quick phone call to DWR, we found out their product support team agrees. Also, if you go with a pro (at least the first time around), you'll find out first hand about the best methods for future cleaning and upkeep for this specific piece.
That said, if any readers have been down this road with the Bantam (or a similar 100% cotton upholstered piece) please let Alex know how you have handled the cleaning - and as always...any recommendations for good local upholstery cleaners are welcome as well!