Drilling holes might be risky, as you could bridge internal ground and power layers.
There's no drilling to be done in the PCB, there's holes pre-drilled and pre-finished in the PCB itself, so you'd only need to align some markings on the heat sink and drill through the heat sink itself.
Then we could add some pressure to the connection with some bolts etc. (making sure of course that the thread on the bolt has a diameter smaller than the hole in the board)
I've actually found the top of the chips get very hot as well so have been considering fashioning some kind of double sided heat sink either with an external clamp around the sides (so the sinks sandwich the board) or a second sink with another drilled set of holes in it.
There is however a transistor that sits in the 4*4 chip grid that sits higher than the other chips, so some consideration for that would need to be taken into account before a secondary heat sink was applied.
As a side note - regarding the separation issues I've noticed that the issue is likely from a lack of cleaning of the PCB from the factory before the heat sink was applied (I'm assuming the manufacturers did the heat sinking too) there was a fine black dust between the heat transfer pad and the PCB which was found after a heat sink came off and I cleaned the board with some alcohol.
If you are using existing holes, then the risk is minimal. I have 4 of these Av16 Drillbit boards, which are stacked with the heatsink on top. So far I did not have any separation issues and they are working quite reliably. These are significantly less efficient than the older bitfury based boards and require plenty of cooling. I'm using 12 cm fans in push-pull from the sides, blowing air through the fins and also some old HDD cooler dual fans on top of each heatsink. This keeps it at a reasonable temp of about 47 deg C. Overcloocked to Av16:int:750:1:1000 they produce about 88 GH/s altogether.