My suggestion is to allow a passenger flying two segments in a day, to purchase both upgraded boarding positions at the same time from original departure destination.
I'm not sure this is feasible. Upgraded Boarding is based on the availability of open Business Select A1-15 positions, and can only be purchased at the gate prior to the beginning of boarding, once the number of open positions is known. Since the first departure on a connecting flight could be hours prior to the departure of the 2nd leg, selling Upgraded Boardings wouldn't be ideal. Southwest would prefer to be able to sell full-fare BS tickets as late as possible. Also, if your first leg is delayed and you arrive late into the boarding process (or after departure) of the 2nd leg, Upgraded Boarding refunds would be necessary, which would add unneeded complexity.
I do feel, however, that at some point Southwest will begin selling access to earlier positions and/or products like Upgraded Boarding when you book your flight. Some sort of hybrid "open seating" / assigned position system, which would generate ancillary revenue and work as a tide-over until the point at which Southwest adopts/monetizes assigned seating.
That is a great idea for plane changes, as long as the 1st flight is on time or the connection is a longer one. It would be disappointing if I barely connected and the early boarding opportunity was lost due to scheduling. May be worth a look though!