Hi Lapponia,
Yes, I did test that both armatures moved freely when I was trying to figure out what was wrong with the relay before I dismantled it. Everything on both relays seemed to be fine, and the only odd thing I noticed was the purple colour of the armature wire on the upper relay as per my earlier picture. If you look at this picture:
you can see that because of where the fulcrum point is, the end of the armature with the contacts on it can move the 1mm or so to close the contact with only a very tiny movement at the end where the wire is. Sorry the second picture is not so good, but you can see that when I close the contact with the pen, the movement at the wire / spring end of the armature is barely visible in the picture; only a fraction of a millimetre, which the wire does not interfere with at all.
I did think about rebuilding this relay with the capacitor you suggest, but it is not possible to get at the fixed contact of the upper relay, the one that corresponds to the burnt one, to clean it up properly. I may get another relay to carry as a spare, and I would certainly put a capacitor on that one and give it a try - unless you get there first!