Welcome to Moen.
The reason that cartridge was leaking was because you didn't have that cartridge aligned in the keyway deep down inside that brass housing.
The job I did recently was exactly the same type scenario and the tool I made out of 3/4" copper was more effective at removing the plastic keeper than the damn Moen tool I bought that's designed to remove it!
The "Moen" tool was slightly smaller and damaging the collar upon removal. I used my 3/4" copper custom built tool and wah-lah! Came right out with damaging the plastic component.
How do you know for sure you damaged the brass housing? You can't judge that by those plastic pieces alone.
There's a rim on that cartridge and you'll feel an indenture, take a flashlight and look deep into that hole where it goes and you'll see that it has to match that in order for it to mesh and provide a water tight seal.
I'd rather beat up the elderly than work on another one of these faucets given the design is just overcomplicated, uses too many plastic parts that allows too much free movement in those handles before they turn the faucet on and off.
Designed solely from the engineer's design table and never to the real functionality of what the homeowner is expected to deal with.
Go to a true blue plumbing supply house and get those parts that are genuine Moen parts and you should be able to get it put back together.
If you decide to beat up the elderly, post it on youtube; I want royalties.
Go to www.Moen.com and see if you can find a parts explosion that details that cartridge going all the way down into that housing.
I sure in the hell couldn't find it and I won't get my 10 minutes of life back either.