Normal behaviour, and you're defeating the transmission doing what it's supposed to do. Running at 4k RPM going up hill will not hurt your engine (and people will be happier behind you).
Peak HP for that engine is over 5,000RPM, and peak torque is over 4k. If you're keeping it under 3k, you're not even in the power band. If you aren't up into the power band, your engine will pretty much fall flat. So, your automatic transmission will shift when it needs to in order to stay in the power band.
Next time you are climbing a hill, let the engine rev. The transmission will select the appropriate gear for the job of climbing the hill, so that the engine will make enough power to climb at a decent speed.
NOTE: The '91 Vulcan engine makes similar HP and Torque, but at lower RPMS. That engine will climb a fairly steep, long grade at 60mph, and hold speed, IF the transmission is in the right gear. (not overdrive, probably not 4th, depending on the hill).