What I've seen with architectural shingles is you don't have to be so meticulous with alignment, like going back a full tab or two. Just cut back a half tab or what ever looks good and maintain a stagger.
Don't use them often but I like my older Crescents. A while back I picked up a Westward from Grainger. Chinese made I think. It's a smooth and tight wrench.
Am man, got pockets, do things, gonna carry things. I always carry a knife, don't always need it but have it when I do need it. Wife or coworkers always come to me to borrow a knife, pliers, screwdriver which I always seem to have in my pockets.
I always have my Leatherman with me but I saw these at HD and thought I would give them a try. They fit my pocket unobtrusively and are easier to deploy than the Leatherman pliers. I think I will have them a long time.
4.5 inch Crescent pliers.
"Unfortunately, my boss does not like us doing modification to tools or equipment."
Buy your own tools and modify them.
There are countless tools out there for pulling and pushing things. Simple bolt and stack of washers has served me many times.
That cap is a repair. I don't know of any that came from the foundry with the cap. I wouldn't call it a poor repair, it is probably from use, the edge gets work hardened and breaks off. Also, a little water will get between the surfaces and with it brings rust that will further the de-lamination.