Broan E64E30SS with Broan's 600 CFM or higher remote or in-line blower will do the trick. These utilize 10 inch round ductwork.

Remote blowers install on the outside of your house, either on the roof or an exterior wall. The In-line blower would be intalled in an attic if you have the room. These tend to be slightly quieter than the remote blowers.

The higher the CFM output a blower has, the quieter its operation on low setting, the most common setting.

also look at Vent-A-Hood 30 inch 600 CFM units. These are a bit quieter for normal and high settings than the Broan but work best when the output from the hood is vertical, not horizontal. Also, if these appeal to you, have a saleperson show you how to dismantle to clean. It's not hard but it's also not for everyone

You say under mounted, but then you say flush mount under the cabinet won't work, did you mean downdraft?

I mean that the ones that attach directly to the bottom of the cabinet that sit flush with the bottom of the cabinet.

These ones can't be used with my current setup.

I've seen one that fits your requirements.
It goes completely inside the cabinet and nothing sticks out.

Here is a link that might be useful: Insert Liner 32