I too have some old pad ones, and some that are old that have deteriorated more than others. I also know that many new synthetic materials are by and large much better than in the past.
The human body can adapt pretty easily to different LOP, though shotgunners have certainly shown that fine tuning said LOP for improving 'wingshooting' scores is not junk science. I dont shoot a rifle like a shotgun so after only a bit of handling I can usually get used to most, and a 1/4 or even 1/2" isnt likely to through me off. IIRC, years ago the Army Marksmanship Unit did some testing and determined that adult shooters could adapt to as short as 12.5" LOP and not really diminish their scores.
So.......I suggest you have a LOP that wont get hung up as you mount the gun and not so long as to make you feel like you are reaching too far for the trigger. Also make sure on a heavy kicker that your thumb at the wrist isnt going to punch you in the chops when you touch it off. There is a pretty fair bit of leeway in that, and one needs it if you shoot the same gun through different seasons with varying amounts of clothes. (BTW, the old butt in the crook of your elbow to your triggerfinger test tells you nothing other than how long your forearm and finger are; I dont know anyone who actually shoots that way).
No doubt. With a rifle I'm a sight user... shotgun is more of a fit to the shooter thing IMHO.
Actually, other than shotguns, been my experience grip angle on handguns is a critical thing for me... not with aimed fire, but definitely with point shooting. Love 1911's, but they point high for me... as though they were designed to hit the bad guy from a hip shot... but say a PPK, P38 or CZ75 points about right. With SA revolvers there's enough choice since it's rounded that it's a matter of practice, but 1860 Army or Super Blackhawk size is what works for me.
Perhaps biggest disappointment for me on those lines was finding out a Ruger Mark 1/2/3 actually points higher than the 22/45 grip and thus the 1911.
I figure my hands or wrists must be unusual since the Ruger Mark 1/2/3's are so popular.
An old bud said it this way... "It's like you should be able to point it in total darkness and hit what you are shooting at."
I've found the "English Theory" or whatever it's called... fitting the gun or anything... even a pool queue to the user has merit if you want it to work "automatically" like that.
But certainly, if you are using sights then it's more a matter of focus.