The speedometer gear is driven off the governor gear. That is a metal spiral gear that is part of the governor shaft. Its not hard to get to if you have OEM exhaust manifolds, but there is only one choice for that part.The standard gear that came in our coaches was 31 teeth (403417) To correct it to a 3.42 ratio you would need a 34.5 tooth gear. Seeing it is difficult to make gears with 1/2 a tooth you would have to compromise to 34 or 35 teeth. that is why they use correctors. In the parts book it looks like the pinion drive gear is part of the rear hub assy. and not easily replaceable. In any case, even if it was, it would be a fairly big job to change that gear. Even if you could get a 34.5 tooth gear I doubt it would fit into the housing.
I have not taken out the speedo gear, but it appears it is held with a bullet shaped bearing assembly which is held in place by a simple bracket. It should just pull out once that bracket is removed.
One thing I don't understand is if you get a gear with more teeth, isn't it going to be larger in diameter? And therefore the shaft of that gear will need to be held further away from the governor gear it is meshing with. But I don't see any reference to this...
You can see the spiral gear just under the governor house cap in this photo:
gov_73s
This governor has been in my coach since I've owned it. I swapped Dans governor and took this one out. It has a purple and yellow spring and the weights look the same as Dan's. Fished out the springs and measured them.
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Here is a good photo of the speedo gear and the associated parts. Just one bolt to remove the bracket and it should slide right out.

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The housing for the driven gear is a steel plug that is sealed to the transmission case by means of an O-ring, and contains a one-piece rubber lip seal that seals to the speedometer driven gear shaft. Here are the components of the speedometer driven gear assembly. Those who have changed their...
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My transmission leaks at the speedo cable so I likely need a new O-ring and shaft seal. And this photo has all the info I need in the comments!!

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A steel wire spring ring retains the lip seal in the speedometer gear module. The seal is GM part # 1240382 which is available at GM dealers. The O-ring is a #117 (.103? diameter with a 1? outside diameter). The groove in the housing is .826? which leaves the O-ring proud when installed The...
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