Thought I'd reply since no one else has.
As you discovered, it would be difficult to redo your lease now. This would require termination of the existing lease and creation of a new one. Not aware of any prepayment penalties but the payoff would be based on the residual and other factors which will probably result in a higher cost basis.
While I'm sure there would be bureaucratic resistance, GM Financial "could" terminate the existing lease and make a new one based on the payoff numbers for the old lease (like a mortgage loan refi) but I think you'd find that your "new" lease payment would be higher than the old one as a result.
So, it would probably be cheaper to just pay any excess mileage fees that you incur than to try to terminate the old lease with the 10k mileage allowance and make a new lease w/a higher mileage allowance.
If you drive 5000k more miles, that would be an extra $1250 at 25 cents/mile over 3 years or extra $416.67/year or $34.72/month, which isn't all that much when you think about it in terms of months. The only problem would be is that you'd have to pay the $1250 as a lump sum at the end of the lease.
If you're diligent, you could bank the extra $35/month in a separate account to use at the end of the lease (like an impound account to hold tax and insurance payments paid over the year to a home mortgage lender who wants to make sure those things are paid, especially if you're a low down payment borrower) but few of us are that disciplined.