Problem with defining stuck projects

[Bob Heffernan <bob.heffernan@gmail.com>]

Dear all,

I am having trouble setting org-stuck-projects in a way that works for me.

My org-files are organised something like this...
* Non-project header
  - blah, blah
  ** Foo
* TODO Project 1
  ** TODO Do this
     CLOSED: [2022-07-06 Wed 17:10] SCHEDULED: <2022-07-06 Wed>
  ** TODO Do these
  *** TODO First thing
      CLOSED: [2022-07-06 Wed 17:20] SCHEDULED: <2022-07-06 Wed>
  *** TODO Second thing
* TODO Project 2
  ** TODO Something
     SCHEDULED: <2022-07-07 Thu>

I want the following:
  1. A project is a level 1 header marked as TODO
  2. A project is not stuck if it has any sub-header that is scheduled but not closed.

So, in the example above Project 1 counts as stuck, but Project 2 does not.

What I've got so far is this:
(setq org-stuck-projects
          '("+LEVEL=1/TODO-DONE" nil nil "SCHEDULED:")

But this will clearly mark both projects 1 and 2 as stuck.
I need some way of specifying the "but not closed" part, but am at a loss as to how I can do this.

Any help is appreciated.
Regards,
Bob Heffernan