Mine is doing the same thing except I can get second gear in manual if use the shifter. The no down shift, and shaking is caused by the torque converter not unlocking. I have not solved mine completely yet, but I am pretty sure it is a lack of brake peddle switch signal getting to the TCU, Transmission computer on mine. It could be a bad brake switch or wires or ground. The TCU looks for a brake switch signal that your foot is on the brake to disengage the TC (which is operated by the third electric solenoid in the valve body, via the TCU computer).
I installed a toggle switch years ago on mine that allows me turn the TC lock up on/off with a dash toggle switch, and in the off position mine down shifts and does not shake!!!!
I would also try a few Dex III fluid transfusions even if the fluid looks good. I have seen Dex III transfusions do miracles with the AW4.
Lastly, you mentioned a snapped axle, et.al., is it possible the vehicle speed sensor or cable was damaged!!!!!! The TCU also looks at the vehicle speed!!!! Also, might check the NSS switch to make sure the TCU is getting the proper D, 3, 1-2 signal.
You may have two problems!!!