From a bonus perspective, that's the better approach. From a credit perspective, it's not necessarily the best approach.

You need to explain your credit history and how this UA card relates to it. If your UA card was very first credit card ever, the answer is completely different than if it was the 20th credit card in your lifetime!

Meanwhile, you can't choose the credit line for a new card. The amount of credit line is assigned the bank. And unless you have other Chase cards or a Chase bank account, it would be better to apply the new card before you cancel the card, to have at least through overlap a continuous history with Chase. But in any case, you may get a different credit limit on the second card, no matter what order or timing you do this in. The only way to be certain you have the same exact credit limit is to give up on the bonus and do the card conversion instead of applying for a new card. The second best way is actually to reduce the credit limit on your existing UA card at least several weeks before you apply for the Southwest card. (It can take weeks for credit limit removed from one card to be available for a new card.)

You need to prioritize these things:

• credit score
• new card signup bonus
• credit limit

because you may be reducing one by maximizing another one.