has anyone successfully figured out how to mimic this painterly style/texture in illustrator (without actually getting out a paintbrush)?
Some things are not meant for some methods.
Styles such as your sample are not meant for Illustrator or vector work in general. Illustrator (et. al) has a targeted use and subtle, random, varied, textures are not its' forte.
While this can be done in Illustrator, the very fact one is using Illustrator makes the work 50 times more complex and time consuming, if not much, much more. With Illustrator, you would need to manually create and define every little variation.
This style of watercolor-esque art is better accomplished in a raster editing application such as Photoshop where all the subtle flecks and transparencies are more organic, natural, and intuitive. You get "happy accidents" when painting, you don't get "happy accidents" when vector drawing.
All that being posted....
Create it in Photoshop, open the .psd in Illustrator and trace it if you must have a vector format. There will be some discrepancies, and the trace may be very, very complex and take some time to process. However, it would be vector.