Control Center - Intake sheet column with a "link in from" from the Profile Data?

I am trying to set up a column in my intake sheet that will be updated via cell link FROM the profile data.

I understand I can use CC to set up my intake to push data to the profile data for a project. I essentially want to do the reverse: update a field in the intake sheet base on a change made to the profile data.

I want to do this to help automate the archiving process. I have my default archive set up to move a project into an "Archived Projects" work space. It will remove all sharing, alerts, and freeze cell links and formulas. It will also NOT move the project from the intake sheet or summary sheet. Unfortunately, the archiving options only allow you to change fields in the profile data sheet, not the intake or summary sheets.

I have a column in the summary sheet called "Archived?" that is just a check box. My archive settings change the corresponding "Archived?" row in the profile data sheet to "true", which pushes to the summary sheet. This is great because it allows me to run reports on archived or non-archived projects, or both. It also allows me to create a filter in the summary sheet to view only non-archived projects, which helps clean up the view.

I'm just trying to get the same thing, but with the intake sheet, in an automated way. From what I can see there is no way to automatically push something from the profile data back to the intake sheet via archiving.

I'm aware that I could create an "Archived?" column in the intake sheet and just manually check it whenever I archive a project, but I want the process to be fully automated. I don't want to rely on someone remembering that step. That will be my alternative if no solution is possible.

I am open to different ways to attack the issue as well. Overall goal is to have archived and non archived projects live in the intake sheet AND summary sheet, and be able to filter reports based archived/non-archived, and the process should be automated through the archiving function in CC.

Thanks!