Seems so simple to just say “let us know when you have 1 hour to do this take home and we will send it to you at that time. Sumbissions will be accepted for one hour after we send you the coding challenge”
I'd say in the list of companies, probably 2% of the 'take home projects' describe that. A one hour question is most of the time the phone screen or the replacement of it with an automated online exam.
Problem solved