Open source, web-based document editor?

Assuming JavaScript is fine for your environment: then TinyMCE editor would be a good option. It is very easy to setup/install and doesn't require any administrative permissions. It is also free/opensource (support offered via bug/feature request tracker and forum - or paying support). (Disclaimer: I'm not a member of the TinyMCE team nor do I have any pecuniary interests however I have contributed a time or two to the source code and have authored plugins for it as well.)

To go over your required features:

• basic editor features, boldface, typography, italics, etc: Absolutely - and it can be configured to do a freaking amazing variety if you so desire; but to be totally functional and effective does not require much config. Try it out or for even better the TinyMCE fiddle (think JSFiddle but for TinyMCE specifically - last I looked some examples were only for the old 3x line).
• understanding images: er I think so maybe - I'm not sure what you mean by this.
• being able to export an XHTML document with images encoded as Base64, inside the document: Yes HTML is the default format. Base64 encoded images can be manually done. I hear there is a plugin that will automatically do them though I haven't used it.
• being able to take input from the cutbuffer (Ctrl-v a Word document into it) (not perfectly, but at least getting the content onto the page): Yeah you can do that - and usually most of the formatting is intelligently copied.

It's possible that StackEdit (or just give it a go) could meet your needs. StackEdit is editor that makes use of "Github flavoured Markdown".

The requirements for the editor are:

• basic editor features, boldface, typography, italics, etc.
• understanding images Takes URLs, and imports from Google+
• being able to export an XHTML document with images encoded as Base64, inside the document ! but You can export to HTML, but also your own custom template
• being able to take input from the cutbuffer (Ctrl-v a Word document into it)
  not perfectly, but you can of course get the content onto the page)

It also facilitates publishing to web (several options), as well as export to PDF.

There's not a lot of green YES's there, but I think it's still worth a look. It really depends on your use case, but I've used it produce some basic but attractive documents when other things weren't handy. It's an especially appealing option if you enjoy drafting in Markdown (which I find very fast).

Ok, so the option I went with was the bootstrap WYSIWYG editor. For those using bootstrap it's an awesome option.

Available for download on GitHub

https://github.com/mindmup/bootstrap-wysiwyg/

It works nicely, and I was able to code my own image-resize feature. It can be styled to fit any project, but has sensible bootstrap defaults. Images are automatically in Base64, so all you have to do is save it as a file and it works completely standalone.