craftgrrl | Handbag Modification Question

Hi everyone!

I've had the urge to make a new handbag lately, but today when I was out running some errands, I saw this bag for a really good price, fell in love, and brought it home. The only problem is that the strap is a little short for my tastes (I like bags that can be worn over the shoulder and across the chest for hands-free goodness), and it's not adjustable.

Anyone have any crafty ideas about how I could modify this more to suit my tastes, without deconstructing the whole thing and installing a new strap? I was thinking maybe splicing in a new section or an adjustable portion, but I can't think of a really good way to do it. Yes, I do have a pretty decent sewing machine.

Thanks for your help!