Hey Turbo, I was able to get to my project TC with the 352 this morning and play around with the tranny. My movement of the shift shaft is the opposite of yours. I can only move it in and out, no side to side movement at all except in one position. It definitely takes a bit of force to move the shaft in and out with a screwdriver in the hole at the end of the shaft. In what I believe is the Neutral position, the hole is 0/90 deg position and I was able to move the shaft in and out with three distinct detent positions. In the middle position I was able to move the shaft about 10 deg CCW (actuate the reverse detent?) and push the shaft all the way in. My 352 has been sitting for at least 20 years.
The first picture shows the shaft in the center position and the middle detent. The second picture shows the shaft rotated to actuate the reverse detent but the shaft in the middle position. The third picture shows the shaft pushed in. What position is your shaft in, if you can tell.