I use a Caradice Nelson Longflap, which hangs from the saddle in back and which I like. But I've never tried to transport a laptop in it and I'm not sure it would work. I'm sure you could fit one into it, but I don't know how much room you'd have left for your clothes and other stuff.

I think it's nobody's business but your own if you build another, buy another or ride what you already have. That said, I think you've got a fine commuter already. You say it's heavy and you'd sweat, but I guess I don't understand your reasoning that you don't want to take a shower for a six mile ride. Don't you shower anyway? What difference does it make if you shower after you get to work versus before you leave for work?