The minimum connection time quoted by Southwest is not relevant to this situation. As you are talking about separate tickets you have no protection if your inbound is delayed. You will need to review what the consequences are if you have to buy a walk up ticket on the day (how much).

AA did use to protect from OW to OW but not sure if they still do or if your situation would be covered.

Personally I am in a similar situation and have booked a night in the airport Hilton.