Hi Barry

I have had vibration in bowls that I did not think should have
happened, however they did and My thinking goes like this, the shape of
the bowl and the wood grain and stiffness that have to overcome the
force needed to cut the wood, sometimes set up a surging or vibration.
I have had more problems with flatter bottom bowl than with curved
bowls, especially the higher side bowl liked to start flexing.
And yes I think your gut feeling to go for a smaller gouge I think is
right, anyway that did help for me, making the force needed to overcome
the cutting edge smaller helps most, by either the presentation of the
cutting edge or using a smaller gouge and sharpening helps some also in
my experience , the problem with the smaller gouge though is of course
that you do have to take lighter cuts and you do have to be able to
keep the tool rest up close.
For finish cutting a dried previously rouged out bowl, going the
stepped way of 1" or 2" at the time is one way of minimizing the
flexing, but keeping a nice flowing shape becomes harder to do, but it
can be done.

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Have fun and take care
Leo Van Der Loo