Off topic but you can deduct cost basis against 1099 income. You report the full 1099 amount and separately show the cost of goods on schedule C or if not schedule C you can add a negative other income item for the cost of what you sold. I expect that either way you slightly increase the chance of raising questions.
Seems on topic to me, the additional information you add is very important, because it is relevant to the calculation of determining proceeds from selling the tickets (vs. just using them). Better to bring this up and all of the details about the potential tax implication now vs. months later when the 1099 shows up.
To me the time element of just tracking all of that data for the tax form, for the sale of some one time flight credits, doesn't strike me as worth the reward. Especially under a scenario where multiple gift cards were used, tickets purchased, canceled, re-booked, credits earned, etc. Too much hassle for too little reward.
Plus the issue of Southwest saying it is against their terms to sell credits. In theory you could sell credits, then the buyer of said credits has some "issue" and turns around and reports to Southwest that someone sold them the credits. Southwest could choose to do any number of things, including nothing, to the person violating their terms by selling flight credits.
Perhaps donating said credits to some credible non-profit organization that doesn't get much funding and can really use them could be an option to get rid of them?