I'm thinking the problem is with the 4-5 clutch(C3) and not the 3rd gear brake band(B4) or servo. If your 2-3 and 3-2 shifts are good then the 3rd gear brake band is applying and releasing as it should. During the 3-4 shift the 3rd gear brake band releases and the 4-5 clutch is applied. If the C3 clutch pack is badly worn or there's a leak in the fluid path that applies this clutch then this could cause a delay in the C3 engagement and the flare during the 3-4 shift.
The reason I mention a possible leak in the fluid path to the C3 clutch is because there are 3 sealing rings involved. The fluid path that applies the C3 clutch goes through the end of the shaft (sealing ring 1) and then up through the shaft to a rotating drum which contains the C3 clutch path and there two sealing rings between the shaft and drum. To help determine if it may be a problem with the apply pressure I mentioned a pressure check in an earlier post and the gauge set needed. The problem though will likely require the transmission to be opened up and repair/rebuilt.
You mention you did another adaptation and previously you're weren't able to get the 3-4 shift to adapt, did it adapt after the valve body replacement?
I've attached some photos of the C3 clutch and the shaft the it rotates on with the 4-5 clutch drum removed, you can see the two sealing rings on the shaft. The 4-5 clutch apply fluid is feed from the shaft up between the two sealings to the 4-5 clutch drum. This drum that contains the 4-5 clutch also has the 3rd gear brake band around the outside of it and when this 3rd gear brake band is applied it holds the drum stationary and sun gear for 3rd gear ratio and for 4th and 5th gear ratio the 3rd gear band released and the 4-5 clutch is applied.








