That is correct, a personal guarantee on a corporate loan does not provide debt basis for an S-Corp.
if I made monthly payments on the corporate loan using my personal funds, could I consider these payments as adding capital contributions or additional debt basis to the corporation as a shareholder even though the note still remains under the corporation? - if you used your personal funds to pay these loans you could take these payments as capital contributions to the the S-Corp. It is not advisable to do the transactions this way, generally you should transfer the money to the S-corp and then have the S-Corp pay the loan. I have seen this done many times though and believe it will hold water with the IRS.
If this does allow me to add to my debt basis, couldn't the corporation pay me the same amount as a loan principal payment? - You cannot take these payments as debt basis. The only way you will get debt basis in the S-Corp is if you loan it money directly. There must be a good paper trail here and perhaps legal loan documentation. Also note that you must charge the S-corp interest on the loan above the IRS imputed interest rates for the year (I believe the loan must be above 10K in order for the below market interest rules to apply)
Or is the only way to let this liability add to my debt basis is by asking the commercial lender to change the note to my personal name? - The only way to get debt basis is to lend the S-corp the money as mentioned above.
Let me know if you have any further questions.