What is the best way to localize a WPF application, sans LocBAML?

Not an expert here, but "littering" your xaml with x:Uids is not worse than "littering" your Windows Forms code with all the string table nonsense you have to do for localizing them.

As far as I understand, WPF apps still support "all the Framework CLR resources including string tables, images, and so forth." which means you can have localized resources.

Of course, it would be much simpler if you created a markup extension that handled much of this nonsense for you. You can find an example of someone doing this here. And there was another, similar solution at http://blog.taggersoft.com/2008/07/wpf-application-localization-pattern_29.html, but that link no longer works.

You should have a look at the article and code available here. It describes different ways of localizing WPF apps, using LocBaml, custom markup extensions, or attached properties. IMHO the best solution is to use the markup extensions and Resx resources. The code contains a localization framework for doing that.