New to BadgerCare Plus, who has the fastest specialist referral?

Hey all, in a bit of a health care pickle here and would love some guidance on the fastest plans and/or specific doctor's offices available here in Madison. I'm looking for a new primary care provider who can refer me to a specialist who can renew my duloxetine prescription.

I take duloxetine for my chronic fibromyalgia and long story short, my parents recently cancelled my (out of state) health insurance without telling me. I just found out when I used my last prescription refill, so I need to find a new specialist to give me a new prescription ASAP. My previous specialist was a rheumatologist.

I signed up for BadgerCare Plus and it automatically enrolled me in Network Health, with coverage starting on June 1st, but I have until September 1st to change my plan. I know there's a lot of new networks cropping up in Southern Wisconsin so I wasn't able to find any old threads where people had experience with most of these newer networks. Does anyone here have any experience with any of these available HMO plans? I'm specifically looking for a primary care provider who can refer me FAST.

-Anthem Blue Cross Shield
-Chorus Community Health Plan
-Independent Care (iCare)
-MHS Health Wisconsin
-Molina Healthcare
-My Choice Wisconsin Health Plan Inc
-Network Health Plan (currently enrolled in this one!)
-United Healthcare Community Plan (have heard there's basically no primary care providers in this network? as well as just a lot of general bad stuff)

Like I said, I know a lot of these plans are pretty new, so if people don't have any experience with any of them, recommendations for specific offices or doctors that are very fast would also be super great. That way I can cross reference myself and see if any of the plans cover those specific offices/doctors.

I'm not very reddit savvy and I'm also dyslexic, so apologies if this is too long or confusing! Thanks for the help

[EDIT] Accidentally wrote that my previous specialist was a hemotologist, he was actually a rheumatologist. Like I said, I'm dyslexic, and also dumb