IMNSHO it is not a distro problem, and I would work with the lighttpd devs, or get on their forums, if not their IRC channel. Two possible leads here and here, The latter has been written by the fine folks at Arch. You might be able to fix that 403 Error (I'd omit the last comma after "octet-stream" but I doubt that that is the showstopper). Pay close attention to the arch wiki and some warnings that make more sense to folks well-versed in Python or httpd/web server setup; I am neither. Good luck.
An alternate approach would be to use the sample configuration provided in the first link, then start tweaking it to suit your specific project. Have one of us here access your website to see if it is operational and functional.
Not having a hard drive is not a showstopper. I was using bodhi as a live medium, but I was informed that although it can be used as such, it is simply too minimalistic. There are plenty of other distros that can work live.
See what you can get from this thread, but nvidia must have something newer than 346 by now. Get your display running properly before adding another screen lol You know, I recall insisting on showing the splash screen aka nvidia logo (via the nvidia control panel) before Enlightenment shows its splash screen--this is after plymouth--just to confirm that the closed source drivers were kicking in. Suggest you do the same, especially if you plan on using more than one display.
If you plan to install the nvidia drivers some time in the future you can use the control panel to set the brightness and the layout of your dualhead rig. It can save your settings if you put a check next to Restore settings on boot. Set it up once, use the module and your Bodhi will be ready every time.
Thinkpads are suitable for linux, like greywizard says, especially when their keyboards don't have that logo on them. It's only when you pick their unique 12-inch models with the unusual configurations that will tax your patience sometimes; I recall trying to get the stylus to work on Fedora, but did not have the time back then.