Thermal tape would definitely improve contact. And once it heats up it softens up a bit and if you press on the heatsink the thermal tape will fill in gaps and scratches on the surfaces much like thermal paste. This is the tape I used.

https://www.amazon.com/gp/product/B07Z25F617/ref=ppx_yo_dt_b_asin_title_o01_s00?ie=UTF8&psc=1

Thermal paste would work. You could also use a high quality thermal tape like the one here.

https://www.amazon.com/gp/product/B07Z25F617?psc=1

Once it heats up it softens quite a bit and you can wiggle your heatsink to work out any air and get it as close as possible to the surface.

Edit: Apparently it's out of stock in that old listing but I'm sure you can find that or a similar product elsewhere :)