I've tried something called "end wire sleeve" (I'm not 100% sure this is the official english name for those) as pins for Z566M/LC-631/ZM1040/Z560M, to be more exact - these:
http://www.tme.eu/gb/details/tul-ni-00508/bootlace-ferrules/ninigi/ . They work really well with Z566M/Z560M, pins have very little free space inside this sleeve. I've soldered them with a broken tube as a reference and other tubes fit in it really well, as long as they have straight pins. LC-631s are a bit loose and some of them won't slide in easily, viva communist times precision. ZM1040s unfortunately do not work with those at all. Datasheets for ZM1040, Z566M and Z560M specify pin diameter as 1,02mm, but only the first one does really have such diameter, Z566M/Z560Ms are more like 1mm. Those wire end sleeves are too tight for a real 1,02mm pin.
I've got one tube for about 3 weeks in sockets like this (changing between two sockets every few days, also I've pulled it out and slided back in multiple times) and it still works, so I assume it doesn't break the tubes due to too much stress on pins.
I think I'm going to risk using those in the future - theoretically they should provide worse contact than any pin that puts some pressure on the tube pin, but in reality due to tubes being used they always have pins a little bit bent in some way, so the contact should be reliable enough for this application - this is no audio signal, some noise coming from the contact can be accepted, as our eyes won't even notice :)