That's what I figured it being an SLT, but the way you described the issues they were symptomatic of a manual.
. What you're describing is almost the same as trying to change gears in a manual without using the clutch.
That being said, I've never dealt with a linkage problem where it sounds like the valve body is keeping it stuck in 1st gear. Just not likely.
I think it's safe to rule out the linkage and concentrate on the valves. That's be a Dealer issue. Not necessarily an expensive issue but in internal issue none-the-less.
Depending on the mileage it's entirely possible that a trans service and a power flush would cure it...should I cross my finger's for ya?