I have fixed up several different kinds of kegs over the years and whilst I can't say for certain I have seen these posts (need more pictures to better ascertain) I would be surprised if they are limiting the flow of CO~2~ into the keg. I do find that sometimes these kinds of post poppets (where they are held in place in the keg post by 3 feet) can be stiffer than the universal kind (which comprise of just the poppet and a spring and aren't held in place by anything) which can require some more fiddly placement of the quick disconnects. A cheaper fix for the posts would be to swap out the poppets for the universal kind (which retail around $2 USD as opposed to new posts which are more in the $15-$20 range USD).
When you say you have tried everything else, can you describe your carbonating process and the things you have tried?