DIYbanter - Lawn Mower Speed adjustment

I have an old (1970's, 1980's) ariens hydro mower. I've got it
running great, and cutting great after working on it Saturday.

The last problem is that the speed controller has a neutral position,
which is sort of a notch, and about 1 foot of room to slide forward
and backward on either side of that notch to control how fast it goes
(in forward or reverse). It's on a stick like a car shifter, which a
black ball on it.

The problem is that when the stick is in the neutral position, the
mower is actually going backwards. When it's about 1/3 of the way in
forward, that's neutral.

I could live with that, however, it will not reach it's max forward
speed, because the stick will not go far enough forward.

Does anyone have any suggestions as to how to adjust the neutral
position?

I tried loosening the shifter where the base of it is clamped with a
nut and bolt to the frame, and where it goes to the transmission. I
could see the device that had a notch for neutral. I loosened the
stick, and moved it back, making sure the notch stayed in place. It
helped a little, but not as much as I needed.

Any other suggestions for what to try?

Thanks.