Try browsing the samba ALX domain from PC1 on the LIVINGEDGE domain. LIVINGEDGE has an outgoing trust setup so it trusts users on ALX. According to the Samba debug traces PC1 authenticates as user "[]\[]@PC1" on the samba ALX domain controller in order to get the browse list for ALX. This results in the guest user password being looked up. So, if you set a guest user password on ALX then PCs on other domains are unable to browse ALX domain. Surely this is a bug?
Please retest against a current Samba release and reopen if the issue is still present.