There are very likely rules and restrictions that I am not aware of, but in terms of the 10-day contracts, there are 52 days remaining the the season after today (Feb 19) based on the season ending on April 12. And my understanding is that a team cannot be under 14 roster spots for more than 28 days in aggregate. They have already used up 14. If you take 14 more out of the remaining 52 days, that leaves 38 days. So each player is going to need to be signed to 3 or 4 10-day contracts, or converted to regular contracts along the way. For Banton, due to service time, his prorated min contract is likely too expensive unless they sign him in the last couple of days of the season. I suspect they keep him on a series of 10-day contracts and then if they want him for the playoffs, convert him on or near the last day of the season.
My guess is that they sign a rookie to a prorated min contract like they did with Amari Williams (0 years of services) or they find another vet that is willing to play the 10-day contract game. The benefit with the 10-day contracts is that you can sign a more useful vet than just some rookie that has never played in the league. In either case, they have very little wiggle room.