Keep Your Shifters
Look...you don't want to begin the slide downward into upgrades yet. Don't listen to folks who tell you to buy Ultegra or whatever. Your drivetrain is currently compatible between all of the components. Keep it that way for 1000 miles, then reconsider what you might want to do.
Bar end shifters are fine, and you will grow accustomed to them in no time. They're kind of nice into the wind, and force you to change hand positions occasionally.
The standard inner shift cable should be no more than $5. Any shop that's higher than that...you should walk out of. One can buy stainless drawn shift cables in bulk for ~$1.45 per cable.
You may be able to replace the inner cable without unwrapping the bar end tape (to expose the housing end (unless it's firmly seated in the SunTour barcon, I can't recall whether there's a simiple flange or some sort of well). Just be patient and observe what you're doing. It's not hard to do correctly. Once you're ready to do the job, post in the mechanics forum, and you'll get instant help...