Mitch, I'd say take your Dopp to your local leather repair shop and see if they can rework the insides. (I know not the cost of a Dopp bag so cannot say if this is cost-effective.)
Otherwise, I can recommend Mulholland Bros. kit bags. http://shopmulholland.com/product.htm?Product=AL303-LAR They make several different models, in several different leathers, with manmade linings. Look for sales/discounts (Sierra trading post &c)
Be there or be square. Only I can do both!
I've got a cat named Beefeater and a dog named Beefeater, and two goldfish called Beefeater and Beefeater. There's Beefeater my hamster and Beefeater my horse, and my piglet, known as Beefeater of course.
Veteran of the Great Irisch Moos Campaign of 2008-09