Anyway, they have many credit cards, most with no balance. Those that do are going to be paid off before the end of the year ($21,000 worth) and their stash of cash will go to that. So at the end of the year their only debt will be the two mortgages (22 years remaining on each).
If most of their cards have no balance, but they still owe $21K, that suggests they have a couple of cards with very high balances relative to limits. These are probably the ones that are hurting them. Of what you have told us, this is probably the biggest negative factor currently. Utilization % across all credit is a major factor in credit score, but so is utilization on a single credit source. If the $21K is all on one or two cards, and those cards are 50% or more of their limit, this will harm their credit score more than having the same amount spread across more cards and all cards below 30% utilization.
My initial thought is to whittle down the credit cards to 1 or maybe two, but I'm not sure. Should this be done? If so, should it be drastic (ditch as many as possible as soon as possible)?
Don't have them do this. Closing cards will reduce their available credit, which will increase utilization percentage, which will substantially harm their credit. Using the above figure of $21,000 owed, it's far better to be using $21,000 of $100,000 (21% utilization) in total consumer credit than $21,000 of, say, $25,000 (84% utilization). Even when the cards are paid off, the statement balances would still be reported on a monthly basis (even if they pay off the entire balance monthly) and having less available credit means they will show a higher utilization at any given time.
This response only addresses the things you have told us... if your friends have made a lot of recent applications for credit, or have missed payments in the past several years, the only thing they can do about those is wait for them to age. They don't necessarily have to age completely off the report-- most single missed payments and credit inquiries have a minimal impact after two years (though this depends on the credit scoring model used).