Sounds like basic internals still ok
That high rpm with little gas threw me off. Sounded like the band was hardy working at all. The two things that change shift point are the vacuum modulator and the speed governor.
The vacuum modulator is on the side of the transmission and has a line that runs up to the vacuum tree on the drivers side of the manifold. Hose should be easy to find. Pull it off and see if there is any oil inside. If it develops a leak, transmission fluid is sucked up. In the vacuum modulator, there is a small orifice that can slow response time if there is fluid in it. Depending how long you have had the problem, fluid may not have made it up to the vacuum tree. A mity-vac on this line with a gauge is a better test to see if it holds a vacuum since there could also be a hose split. This would also effect shift points in other gears. Any engine problems would also change the vacuum.
A shift point change in only first to second indicates that the speed govenor is sticking. This part is located in the extension housing between the transmission and the transfer case. I wondered just how hard it is to remove the governor from the transmission while it is still in the car. So I decided to take mine out of my 92. Removed both drive shafts, and dropped the cross member holding the transmission. Support the transmission with a jack. After removing the bolts to the transfer case, I pulled it out a little an let it swing down. Then I pulled it out more and let it drop to some folded carets. Had to remove the tranny mount to get at the transmission extension bolts. Transmission extension bolts to the transmission and mounts the transfer case. The only internal connection is the parking pawl. The governor valve is then just mounted with two bolts. If you are talented and lucky, you can probably pull out the valve without removing the extension housing.
Remove it carefully, all the pieces will fall out. There is the outer weight, close to the shaft. followed by a spring, then the primary valve that goes into the governor body. The steel valve gets little scoring marks on it. Valve should move freely from its own weight.
Although mine worked, it was very sticky. You could see wear marks on the steel piston. I polished it by hand with some very fine wet or dry paper and oil. Also the aluminum surfaces. The piston now operates freely. If yours is sticking, it is because of wear and not contamination. I think I have seen this part new for about $30.
Not a hard job at all. I think a lot of these are on the brink of failing. The only tricky part is getting the parking rod back into the extension housing. Remove the shift cable so you can operate it yourself from under the car. Put in park to extend rod, then shift slowly into low to bolt on the housing.