My first answer is "contact support" I checked and while they are turned on for our system admin profile, they are not editable.
Alternatively, you can clone the system admin profile to create a custom profile with the same access, modify that profile with the permissions you want and then use that as your new system admin profile for all your admins. This saves the effort of assigning a permission set to every new admin but detaches you from the standard profile. I'm not sure if that would cause any issues or not but theoretically you should be fine.
Some users have used permission sets but I don't think that'll work in your instance as you said you can't currently make any changes because you already have the 2 permissions set to true. In that case a permission set wouldn't be evaluated when trying to save a profile so it wouldn't help you.
A bit of research shows that this issue has occurred many times over the years with different sets of permissions (most commonly, the ability to deploy change sets). In some situations support cannot help and simply recommends the alternative answer I posted above. I just wanted you to be aware that support has shown a history of not being super helpful here so that you're not surprised if they can't help but I would still start by contacting them IMO.