That shift from 2800RPM to 3000RPM is the torque converter unlocking in 3rd gear. Run the transmission to long with the torque converter slipping and you will heat the transmission fluid. Get it hot enough and that is bad.
Any tow vehicle that I had that couldn't pull hills with the torque converter locked I had a tranny temp gauge added so I would know if and when I had to shift it to the next lower gear or slow down for it to lock back up.
It all depends on how long the grade is and how steep it is if you force it to second.