That kit is a great value if you're wanting to not only overhaul, but improve the shift characteristics of the transmission. I don't know if you happened to stumble across the thread by Mike mayben in which he details the band adjustment procedure. It is also explained in the service manual if you happen to have one of those. The 2-3 or kick down band adjustment is accessible on the outside of the trans without needing to drop the pan. It does require a small socket with a specific number of points and an inch/pound torque wrench or a small foot/pound wrench that is capable of an accurate setting of 6 foot pounds (72 inch pounds). That's not much torque. There's a slim chance, but one worth exploring, that putting this adjustment back in spec if it is way out would cure your ill. Usually, a problem with this band will exhibit itself as a missing 2nd gear, which isn't your symptom. Aside from that, your next step is pretty much looking like unit removal for tear down, cleaning, inspection, and reassembly...or replacement with another unit. If you do decide to pursue another unit, there are some things to keep in mind.
1. If your Scout is a 4x4 model, then the donor unit must be from a 4x4 sii also. If your Scout is 4x2, then the donor unit must be from another 4x2 sii, or from a full size d-series pickup or Travelall in either 4x4 or 4x2. The reason is because of differences in the output shafts and tail housings. 4x4 scouts utilize a married transfer case that requires an adapter housing and different output shaft. The full size rigs require the normal output shaft and tail housing. In 4x4 configuration, a divorced transfer case is used, so there is no need for the adapter housing. The output shafts and tail housings can be swapped around, but it requires complete disassembly of the transmission.
2. Its often difficult to accurately assess the condition of a "used" transmission. You don't want to end up spending several hundred bucks on a donor that turns out to be in as bad if not worse shape internally than the one you've already got. If you can't be provided with trustworthy history on a used one, you're basically looking at nothing more than a builder core. Unless it can be had for next to nothing, I'd steer clear. You've already got one of those.