You're not upgrading with miles in the traditional sense (mileage upgrade awards) as that would require calling DL and, if the right upgrade inventory is available, shouldn't be affected by having paid with gift cards. You seem to want to use miles as "pay with miles" to cover the difference between the coach fare you purchased and the current FCM fare offer for FC. However, these usually require odd numbers of miles, so I'm less confident about my statements. FCM offers are dynamic, so DL could have sold some FC seats on your flights in the meantime.

OTOH have you checked G A P fares for your flights? These can sometimes be cheaper than FCM and if it's within 24 hours, your current tickets can be cancelled for free. BTW, I believe the deadline is still midnight of the day following ticket purchase in the time zone of departure, not literally 24 hours.

Since you're a DM, start by playing around with delta.dumb searching for discounted/nonrefundable FC fares and then call DL using HUCA if needed.