The issue with paste is we can't guarantee it's completely insulating the heatsink from the ASIC.
What about those old school mica heatsink pads? How's their thermal conductivity? I googled around and couldn't find any numbers.
This is what the website says of thermal grizzly:
Is Thermal Grizzly thermal paste electrically conductive?
"Conventional" Thermal Grizzly thermal paste, such as Aeronaut, Hydronaut, Kryonaut and Kryonaut Extreme is not electrically conductive. Only Thermal Grizzly Conductonaut (liquid metal) is electrically conductive.
From my own experience I can say that there is no issue with the electrical conductivity. I have done some custom water-cooling project, where I basically drowned some small components in thermal paste because it was the only possibility. I never had any issues form it. I can however not say what kind of thermal past it was. It would in general at least be an option that could be tried out.