I am right now running 6 BM1397 in the R909 that Skot linked to you earlier, producing 2.133Th/s at around 100W. So you need 2 chips at 350GH/s each and those will pull about 30W together. Giving them more juice just makes them run too hot and getting less efficient.

Thermal paste would still give you contact in some areas. It is just meant to fill tiny imperfections in the metal of heatsink & chip, not to create an electrically insulating layer between them.

Maybe look into graphite thermal pads. They have very high thermal conductivity (like paste) and I believe low electrical conductivity.

You could buy yourself an R909 and open it up (I won't do it with mine); I see 2 beefy heatsinks, one per side of the PCB. It has 6 chips. No idea how sidehack did it.