My output from flash/photoshop seems to be a little different from yours, but seems to work if the paths are correct. Test item is here just to give you some hope.
I don't think there is any need to put absolute paths ssl or not, in fact I think they need to be relative to the document, as that is (as far as my example is concerned - xml path anyway) written into the actionscript inside the flash.
Not very helpful, but I do have the lightroom plugin somewhere, which I will install and then I will be able to duplicate your setup, and try for an install. When I do that (and if it is successful) then I will itemise the steps I take to make it work.
That won't be 'til later this evening, or the wee small ours though.
In fact, could you output the files again from your lightroom slideshowpro (leaving the paths just as they are created by SSP), zip the folder (html, xml, gallery/images folder(s) ) and post it here?
If it is too large to upload, then email it to me at neil (at) yeractual (dot) com.