You are correct that if you enter a code different than what is in Box 7 of your Form 1099-R it will cause an issue. It won't match IRS records and they will send you a letter proposing changes to your tax return. You can't make the amount of your distribution that exceeds your basis non-taxable with a code J in Box 7. The only good solution to your issue is for Vanguard to issue you a corrected Form 1099-R with Code T. You might want to request a supervisor or manager if you can't get the issue resolved with a customer service representative.
Another, and much less desirable option would be to report your current 1099-R and use code T in box 7. When the IRS proposes a change to your tax return to make 100% of the amount of the distribution in excess of basis taxable, you can respond and argue that it should not be taxable because of your disability. I don't recommend this approach.
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