Lloyd,
Welcome to the forum! This is a great place to learn and to share.
On your cheddars, I think we need more information about the recipe you are following. Very soft may suggest that the curds have retained a good bit of moisture; cut size, heating, and stirring -- NOT pressing -- are the main factors in how much moisture is expelled from the curd. Pressing does remove some whey, of course, but at this point the key is to get the curds to knit together while still allowing any excess whey to be expelled. That means that one cannot simply bang on the weight from the start; you have to work your way up to the final pressure, giving time for excess whey to make its way out before the rind seals it in.
As Raw Prawn says, higher psi is used only as needed to get a good knit. That said, I've needed a good bit more than 1.5 psi to get a good knit on my cheddar makes - I find that my cheddars do need a lot more final pressure than a cheese that isn't milled and salted before pressing, and conversely it always amazes me how little psi an alpine style cheese needs. For comparison, with a cheddar I generally start with, say, 20 lbs applied to my 7" mold (~.5 psi), and work my way up to 300 lbs applied (~7.8 psi), but for a swiss/asiago/parmesan/etc., I start with 4-8 lbs (~.1 - .2 psi) and end up with 20-40 (~.5 - 1 psi) at the very most.
I also agree with Raw Prawn that any cheese tends to "barrel" to some degree as the rind dries, but I certainly get less of that with cheddars than with something with higher moisture, like a gouda. Of course, one factor is how much you let it dry -- are these natural rinds, or do you wax or bag them at any point?