We have a couple of things going on that make me question if the advance in the slots is truly linear.
The spring force component acting to pull on the weights increases as the weight moves out. (This is great because acceleration increases the centripital force exponentially.) I don't think this bears directly on whether degrees in the slots are linear but helps us think about the geometry.
At complete rest, red arrow representing spring force. Even if there is tension on the springs, they provide practically no resistance to the weights moving outward.
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Now lets put the governer in, creating the initial tension.
The weight's pin moves a little out and a little bit clockwise.
A small component of the spring force acts to hold the weight in.
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Now lets look at the movement.
Install the governer and the pin moves mostly outward, and just a little clockwise
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Move the wieghts further out, and the pin moves almost the same amount clockwise as it moves outward.
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The further the weights move out, the more degrees are advanced for a given distance the pins move in slot. At least that's how it looks to me without actually drawing it out.