My '96 had that problem a short time ago. :{ I dropped the transmission pan en-route to troubleshooting the governor solenoid and discovered a loose part in the bottom of the pan.

The front band adjustment had been loose enough to allow the part that supposed to be between the end of the band and the adjustment screw to fall out. Like you, I could play with the accelerator and eventually get it to shift out of 1st, but since it could never go into 2nd, the transmission was apparently skipping 2nd and going directly into 3rd.
I pulled the valve body down to gain access and put the piece back into place and adjusted the band properly (consult your shop manual, but for 47RE in my '96 it is snug the adjustment down to 72 in-lbs and then back off 2. 5 turns) and haven't had another problem. :-laf I'll attempt to attach pictures... PM me if you want higher resolution on any of these.
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