Not SWA but I bring my Yamaha Silent acoustic on the road all the time. KCM is no issue at all. If folks can bring a cello then my guitar won't be an issue.
I don't see the issue with asking the crew to keep it on the flight deck, I always ask the crew to do just that. Of course I'm usually on company metal so that might make a difference with company rules nd such. I'm sure if you were JSing and sitting up front they'd allow you to stick your suitcase up there so if there's room I see no difference.
Otherwise stick it in the overhead and ask the FAs to help you out if it gets full.
Where are you putting the amp?