I have just bought 2 Samorga liners one for my Red Onion Bays which was a bit slouchy and another for a slouchy Alexa. They are really brilliant, not tacky at all, made from thick felt in loads of colours,really compliment the bag. They are made to measure for bays so a really tight fit and give the bag far more structure.
It will obviously help enormously with the body of the bag and maybe help the flap lay a bit better over a firmer base.
The flap is the biggest problem, When you store it a piece of cardboard cut to size and placed to line the flap really helps. It will make it look lovely and curved again but expect it will flop when removed. Can't think what else to do there, hope someone has some ideas for you.
Link to the liners
http://samorga.com/product-category/■mulberry-bayswater/
That's such a difference to your bays! As you're in the Uk too & these come from the US, I was just wondering did you get charged import tax too by customs?