2130 movement question

[ado213]

Hi all, new member here seeking some technical advice.

I have a Rolex 2135 here with rusted autoreversers 2130 -540 part number.

I am aware there are two types of these, they call old and new style. The new style having the pivot fixed to the outer wheel and the old type having the pivot stud fixed to the inner wheel.

As far as I am aware both the old and new type carry around 77 teeth on the outer gear and 12 on the inner steel gear. I am now told there is a third type that has 55 teeth on the outer gear an 10 on the inner.

I have some of the type 3 here and they will not fit into the original auto wind bridge as they are too big in diameter, not much but you can see the jewel holes are around 1/2 a hole out

Could any of the techies here pass comment, 1) are there 3 types of auto reverser ?
2) if the third option is used, would you need a new autobridge along with associated gearing

thak you guys all comments appreciated