Different Membership Status Rules for Different Memberships?
You can't do this with out-of-the-box CiviCRM and I am not aware of any extension that provides that functionality.

As I am not a developer I can't comment on how difficult it would be to write an extension to provide what you would like, however, even if it is an easy task, extensions need to be maintained as CiviCRM is upgraded.

Grace periods have usually been arbitrarily determined at some time in the past   so in a situation like this is I would go to the parties involved and say something like "Managing membership with CiviCRM will deliver lots of benefits, (enumerate) but the grace period is going to need to be standardized across the organization." and leave it to them (or the common boss in their management chains) to decide whether it will be one or two months.