Just use some adhesive thermal tape. I use it on multiple CPU's without problems. It's properties are ok but not as good as good thermal paste of course but that is not really a concern on lower end CPU's.

Thermal paste is not really needed on lower end CPU's. But I do use it if I can use use clips, screws etc.

It's not a major issue if the CPU is not 100% flush with the socket, there are some socket 3 variants where you just cannot push the CPU all the way down even without the heatsink clips getting in the way. Other heatsink solutions use a plastic frame that goes between the CPU and the socket, effectively introducing a gap between them... that's just the way these things are expected to work.

But if you're worried, there's plenty of alternatives: use thermal tape or other type of adhesive, use one of those metal clips that attach to the socket tabs, some coolers have tabs that press only the sides of the CPU without going underneath, etc. etc. In any case, thermal paste is not really needed for 486, if you want to add some then go ahead, but as long as there's proper contact between CPU and heatsink it's more than enough and paste won't make much of a difference.

Most socket 3 CPUs have offsets on 4 corners of the pins, which should prevent full insertion any way. I see such an offset on your CPU. Why do you want it "all the way in"? It doesn't need to be. To some minimal extent, the 1.5 mm air gap may also help with heat transfer.

I never use thermal paste on 486 CPUs unless using a peltier cooler for extreme over clocking and running the voltage high.

Excellent, thanks for the comments. The CPU posts completely fine even with that slight gap where you can see the pins going into the socket. I was just concerned with it not being flush aka "all the way in" that it might introduce some sort of instability etc if the contacts are not 100%. But I will leave it like that and see how it goes..

A more interesting question might be: why were the 4 corner offsets used on PGA CPUs to begin with? The manufacturer wanted to ensure that users didn't fully insert these CPU's. I don't know the official reason, but speculating, the reason likely stems from the days of non-ZIF sockets. They probably wanted to leave a gap so that people could insert the CPU removal pry bar.