The grease is there just to prevent corrosion, so you dont need loads on there, just a thin film.
Try cleaing out the seat tube a bit and just put a little on the seatpost itself.
If that doesnt work you could get some carbon grease. This has some grit in it to increase the friction on the post.
If the post slips without grease, then it aint gonna be any better with grease.
I’d deffo give carbon grease stuff a bash. Perhaps if that doesnt a bolt up seat clamp might be better. Thomson ones are supposed to be good.