2002 Acura MDX MDX transmission replaced

2002 acura mdx, transmission died on highway in the middle of a trip. Vehicle wouldnt go over 40mph, 4000 rpm. Check engine light came on, D5 light flashing. Pulled vehicle over no reverse after shut off and restarted. Disconnected battery, touched terminals together, same exact thing. Had vehicle towed to shop, codes p0700, 28-01, 41-01, and 45-01. I was told bad transmission by shop. Purchased my own from Autoiweb. Com, A "new" reman trans. With new torque converter. Latest updates to TCU. Installed, reverse came back, no 4th or 5th gear. I am aware of the TSB recommened new ECU. I am aware that 2001-2002 are non reprogramable. I have read, however, that the update PCM should not affect the drivability but longevity. I am hestitant to purchase new PCM if not needed but am unsure where to go from here. Shop feels that I should replace PCM and go from there before deeming a bad trans.