There's a lot of contacts around the die to worry about if you put a liquid metal on there... unless you apply a conformal coating or something to all that first. You'd wanna try that before you glued the lid down really well of course.
I'm not sure if the "grey RTV" type stuff is just a firm silicone or whether that offers further thermal coupling from the heatspreader either into or out of the ceramic (Heat won't travel very well horizontally through ceramic, but it might be worth a bit of dissipation to have it going through it to the ground pins/ground plane.)
But why stick the stock heatspreader back on? Copper plate!
Unicorn herding operations are proceeding, but all the totes of hens teeth and barrels of rocking horse poop give them plenty of hiding spots.