The old version was working properly then just started showing this message, so I upgraded the client. Firewall has been set to allow the client and is even turned off.
I added 3 of those nodes, still the same issue. It is showing 6 active connections just 24 hours behind and No Block Source Available.
If you check the peers[1] do they have >348535[2] blocks? Are you missing ~144 blocks in comparisson to the peers? For all you are saying you should be synced, but the client seems to be confused for some reason. Wrong date settings maybe?
[1] Help -> Debug Window -> Peers -> click a line in the table, see details on right
[2] obviously this is constantly changing, check a block explorer e.g. blocktrail.com for the current number of blocks.