actually with slip the rpms would go higger, not drop. all im gathering from what you posted is that the trans is able to shift while going up a hill, sounds pretty normal. the trans does have a clutch in the torque converter, but unless it comes on in 2nd which its not supposed to do, normally they dont engage while going up a hill depending on the grade or road speed of the car.
the computer has to have the right information to send signal down to the trans for it to engage the clutch in the torque converter.
i seem to notice when doing a diagnostic and seeing that the customers complaint says that the trans is slipping has ranged from the torque converter clutch not engaging, to the engine running poorly and down on power. on the other hand, there are truly times where there actual clutch plates burnt, or a band that can show that the trans was indeed slipping.
since theres not much a code scan can do for this particular car based on the year of it, the best suggestion would be to take the car to a well reputed transmission shop that has a good driveability technician who can tell the difference on whether you have an actual trans problem or possibly its and engine related issue.
on a side note, have you checked the fluid to see if maybe its low and took a sniff on whether or not its possibly burnt?