Just to let you know what I did :
- I recreated the sites in the new Alfresco installation with Share;
- I exported each site space individually in Alfresco Webclient
- In the new Alfresco Webclient I deleted the content of the site Space;
- I imported the content from the export into the new server;
The content came back without a problem ! It may be tedious if you have many sites, but for a couple of sites that worked great !
Steve