Check out any of the Asics motion control (stability) shoes. Decent cushioning, good arch support (which is really where the stability happens), and good pricing. I use the Gel Cumulus 16 model, which is more of a hybrid between neutral and motion control.

Not sure you can get exactly what you are asking for. Hoka's are really cushioned, but motion control requires some arch stiffness.
I have had great luck with the Brooks Ravenna and the Asics GT 2000's. Decent cushion and great control.
Cumulus has great cushion, but is a neutral shoe.

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Team Zoot So Cal

Asics Kayano (latest version only)

"Rides" very soft, but plenty of "motion control" with a midfoot bridge and medial posting.

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Fatigue is biochemical, not biomechanical.
- Andrew Coggan, PhD

The Pearl Izumi H3 road has a 30mm stack height and is a stability shoe.

I've never tried the H3, but I really like the N3, which is a similar shoe without the stability features.

There are also some Hoka shoes that they categorize as stability shoes on their website.

x2 for the Asics Kayano.

Whatever the women's model of the Brooks Beast is the shoe you want. The Beast is a great shoe by any measure.

I would suggest trying on a pair of the New Balance 1260v5.

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Larry Lahodny
Owner, Gizmo Socks
Henderson, NV

The ones that fit you the best.

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Civilize the mind, but make savage the body.

- Chinese proverb

there's always one...