I don't have a dutch press, and all my pressing is done by stacking weights on top of the mould. As a result, 2.5 PSI is my maiximum. The early flips and salting help with obtaining a closed rind, with the salting during the flipping helping to add the saltiness that caerphilly is known for. Much of this salt will wash off during the pressing as the whey is expelled, but that helps bath it in a whey brine. Once you are at the overnight stage, just press with as much as you can. My caerphilly tends to have small mechanical openings due to my limited PSI capabilities at the moment.
A while back I found an old newspaper article (from 1907) on caerphilly. Farmers in New Zealand were making it for market in the UK. Caerphilly, because it went to market young, meant there was much less waiting between making of the product and being paid for it compared to cheddar. I copied it out, and I've attached it to this post. As you can see, they used to press with 5 - 6 cwt (hundred weight, which was 112 lbs in the UK and New Zealand, but 100 lbs in the US), and later work up to 10 or 15 cwt. They don't mention sizes in this article, but I see in my notes I had found referneces to traditional sizes (10 inch diameter), and so these pressing weights worked out to about 7-8 PSI, working up to as much as 21 PSI. In other words, don't worry about over pressing.
I keep meaning to have a go at making caerphilly following the notes in this article, and I think that will be my first cheese in the new year. My cheese making is on hold until then. We're going to be away for a bit, and a fresh cheese would not be happy without daily greetings.