Your new run sounds wonderful - how many are you planning to keep in it? I agree that a smaller mesh size would exclude, not only smaller predators such as rats and mice and stoats, but also wild birds which could get through 2" mesh, pollute the water, steal the food and introduce red mite from their feathers. Might it be possible to cover at least the bottom of the sides with cheaper, thinner, small-sized chicken wire, relying on the weldmesh for strength but preventing small animals and birds from walking in?
I would be more concerned about the top of the run, as foxes can climb a 6ft side and get in from above, wherever you do at the base, if it's left uncovered. Also of course any kind of bird can get in at the top, though with a lovely big run like you have built I don't know if covering it would be practical. When you say 60 metres, do you mean 60 sq. metres, or is that the length?
Are you going to divide it so the hens use one part at a time? Any chance of making it Fort Knox at one end, for when you shut them up last thing at night and early in the morning? Maybe you could roof part of it to provide extra shelter and a dry area for them?
Are there likely to be any problems with your neighbours on the plots if you do instal effective electric fencing as a backup? It would be good against two-legged predators as well as foxes, though, wouldn't it?