thermal conductivity is impacted due to height of thermal path so, dont exceed 1mm so still stays in a good small size and then you dont need crazy high conductivity pads 20+ and a 13+ will do a great job, 0.5 can be very thin and can get easily damaged so a .75-1mm to my experience is a good choice and still will effectively conduct heat to the heatsink.
Thanks, I think I will order a set of these Iceberg pads:
https://www.iceberg-thermal.com/product/consumer/thermal-pad/driftice/. 80x40 should be a near to perfect fit, just need to cut the length a little. Hope that I won't mess up with the upper heatsinks' thermal pad when re-screwing the bottom heatsinks...
Actually the unit is running very well at the moment, but I don't think I can leave it now without these pads attached, now that I know of the air gap.
It's like @n0nce has said, this neat device makes you want to tinker with it.

@sidehack: Would be great if you could share details on the thermal pads used for the upper heatsinks.
The upper are 0.5mm 20w/k. the ones you selected are ok for the back plate, these can be an top plate option as they are 20w/mk and they have different sizes so you can order 0.5 just in case and if you see ok to have both the same type then a 1mm (the pads can be cut with no effort with regular pair of scissors, so 1x0.5 will be enough for 1 unit top plate the two heatsinks, and also will work the same to backplate) :