Shiloh Cabinetry...in either framed or their frameless line Eclipse Cabinetry by Shiloh. Shiloh will do custom paint colors for an upcharge.

Shiloh offers White Oak in regular cut, quartersawn or rift cut.

Medium to Upper mid range for cost....I would say close in price to KraftMaid Cabinetry.

Look into Great Northern cabinetry. They are from the midwest. Hopefully they have some dealer near you.

Ikea has Vedhamn which uses European white oak, a different species than the quercus alba found in N. America.

Pick wide drawers for lowers.

White oak is the most expensive cabinet wood other than walnut. Your statement about paying "a little more" is not realistic. Nor is saying "It's probably an upgrade", because white oak is a big upgrade. What you call "outrageous prices" may simply be what white oak costs, and that's the bottom line. If you are not comfortable with the cost of white oak, then have your island be painted white like the rest of the kitchen.

Contact a local Chicago cabinet company called Builders Cabinet Supply. Their showroom is in Lombard. They manufacturer their own cabinets, so there is no middle man or massive network. I'll provide a link to their website, but their website is pretty terrible - they are a local company and do not have a sophisticated social media or internet presence. So call them on the phone, or go to the Lombard showroom.

https://www.buildmykitchen.com/kitchen-cabinets/

I’m in the west suburbs of Chicago and did a full kitchen remodel last year. (Also got cabinets for two bathrooms and a wet bar, so lots of cabinets.) My cabinets are from Romar down in Channahon (contact/ owner is John). I also visited StyleLine in Lockport, contact is Nancy. I'm sure either place could do white oak, but you'd need to call to verify.

Both places have very good quality and for custom cabinets I think the price was very reasonable. StyleLine has a nice showroom with lots of built-ins to view; Romar also has a showroom but not quite as big. I ultimately went with Romar because at the time the lead times at StyleLine were longer. My contractor did the install but Romar has a guy whose entire job is to come out and adjust all the cabinets and hinges until everything is just right. I worked with a designer so she did the layout and I can’t speak to either place’s design capabilities, but I’m extremely happy with my cabinets.

If you decide to visit either place, I'd call to set an appointment.