What? Don't grind your case for that!
If a 13-tooth sprocket doesn't fit - return it (or sell it), and work out something different.
What gear combination are you trying to achieve that isn't possible with a 9, 10, 11, or 12-tooth front sprocket?
Are people having trouble finding rear sprockets, or something? There are kids quad ones that fit...
+++
If a 13-tooth does not fit without grinding, the tuner's spreadsheet should be updated to say as much.
Could someone confirm that this is definitely the case for all Minarelli cases?
+++
Okay, there is one reason to go big - the more teeth on the front sprocket, the better it engages the chain.
This will reduce wear over time. Slightly. I don't think you had a huge chain-wear problem with your 9-tooth, so a 12-tooth will be an improvement.
It will be even more of an improvement if your rear sprocket has an even number of teeth, but I really don't think that chain life is why you're re-gearing...