Screen sharing while screen mirroring to a TV

I'm teaching a hybrid class this week and next, with some students in the classroom and some at home participating via Zoom.  We have a big TV in our classroom, and I would like to use my iPad and apple pencil to write on pdfs of worksheets that I've got on my iPad and cast that to the TV in the classroom while also screen sharing on Zoom.  That way the students on Zoom can see all of the work I'm doing and the notes I'm taking on those worksheets, and the students in the classroom can see it too because they are watching all of this on the big TV in the classroom.  I know I can screen mirror my iPad onto the TV when I'm using Zoom, but whenever I try to screenshare, it says I'm not allowed to do that.  It says screensharing is not allowed while apple airplay, etc, etc, and screen mirroring are in use.  

I know there has to be a way to do this, because I know teachers who've had to do this - or something like it - all year last year.  I know you can do it with Zoom Rooms (found some stuff on this site about that) but I don't know how to use Zoom Rooms.  And if you have to get them to mail you some contraption in order to be able to use Zoom Rooms, I won't be able to do that (class ends at the end of this week - very time-sensitive issue).  Can anyone help?