I have no duck experience, and I haven't read very many of the duck threads either. So I'm going by "chickens do this" and a big chunk of guessing!@NatJ, I sure miss @Miss Lydia ! I don't really know who our other duck experts are. You were the only one that came to mind.
I know chicks (baby chickens) can be brooded in the coop with a heat lamp, so I'm assuming that ducklings can also be brooded in the coop with a heat lamp (basic idea: as long as you meet their needs for temperature & safety, it does not matter what building they are actually living in.)
If putting a heat lamp in the coop is possible, I really think that will be the easiest way to brood that many ducklings.