Could your SFDC admin set up a wall that until a specific field is filled in the lead won't sync to SFDC?
In our system, without a company name, the lead won't be passed on to SFDC and therefore, the sales reps. When the fills out a longer form with the company name as a required field, then the lead will be passed on to sales.
You could create a new field "First to know campaign" and when the leads are done with that campaign, set up a flow action to mark that box and then sync the lead to SFDC.
Good luck! Let us know what you decide to do!