Are you attempting to get the lender to let you off the hook for the $100K as part of the short sale process, even though (as you point out) you now have a recourse loan?
Based on your post, I assume you have the ability to pay the balance (even if over time) if you chose to. I’m not advocating that you do, I’m just curious as to whether your lender will “go after you” (whatever form that takes) for the unpaid balance. Since it is a short sale, and not a foreclosure, they may have a long SOL before you are “free and clear” from the debt. Plus, who knows what document they will spring on you to sign as a condition of closing.