Where I do my research, in Sweden, there is an abundance of same-name people, even same-name people who do not just live in the same parish but also in the same village. There's a wide variation in the information included in death book entries. When we are lucky there are long obits, mentioning birth date, parents and marriages. In later times, say from 1800, there is almost always a birth date as identifier.
But of course there are also cases like what you are describing, where you just don't know by looking at the death record which one of your Anders Larssons it belongs to. Then there's really nothing for it but to research them all. Well, I find that it usually boils down to two eminently confusable individuals - where the one with the most genealogists among his descendants will have been assigned the easiest-to find death date. Not always correctly.
Working on families, as you are doing, must be the way to go - piecing together all the relevant information. Like: did one of them actually die in infancy? Or did one of them have children well after the death date in question?