In my league every team can keep up to five players. You don't have to, but there's no extra benefit to not keeping a fifth player. Draft is like yours, worst to first.
How do you determine keeper cost? In our league, each player costs a draft pick two rounds higher than where they were kept/drafted the year before. Even though the worst team is slotted for the first draft pick, if they keep a 1st round player they may not get the first overall pick. Managers use different strategies. Some like to keep lots of late round players so they have early picks; others like to stock up on top tier expensive talent. Which strategy works better varies from year to year, depending on what other managers do.
Making your keeper system a little (just a little!) more complex might help satisfy your owners.
"The game has a cleanness. If you do a good job, the numbers say so. You don't have to ask anyone or play politics. You don't have to wait for the reviews." - Sandy Koufax