I went and bought a new bag yesterday. It’s black, and either leather or pretending to be, and it’s only slightly smaller than the straw bag so I can happily fit everything in it. Plus it sits up straight and has many internal pockets, so I can use it as a purse; I tried to do the thing with cutting down on my stuff in my purse, but it ended up that I was just carrying two bags instead of one, so I think I’m going to bow to the inevitable on this one.
The really great thing is that the straps are long enough that I can sling it over my shoulder. I like the straw bag, and always get compliments on it, but those wooden handles are killer for carrying it any distance at all, especially if I put enough stuff in it to use its capacity.