If you only have one "PNR #" (confirmation #) for the origin date of flight, then Southwest's system removes everything when you try to make any change. They cannot comment-off an initial segment off online, they cannot do so via phone, more importantly when they delete your PNR # as a no-show, they will be deleting any attached segments for the origin.

If you really want to push this issue further then call reservations and keep asking them to give you the shorter route at the cheaper price (from the longer route).

You've gotten good advice on this forum so far. The plan won't work and you'll get a long beep and not be able to board the plane. At best the gate agent will pull some strings, make some calls, and get you on the flight without any extra $$ as a courtesy. BUT more likely you will end up missing or delaying the flight. Plus you'll be the absolute last to board.

Since it's likely documented on your PNR Record that you have been given conflicting advice from the reservations phone # perhaps calling and nicely asking for a supervisor will result in some special fare tricks to offset the difference in published price??? Waiting till the day & time of flight seems like a very bad plan. There are a few irr-ops scenarios which could arise and backfire even more: your origin segment gets cancelled but the 2nd segment does fly afterall. your origin segment is late so they shift people to a different flight plan which skips or changes your connecting city... both of those would result in your tickets being modified by the origin flight time.