In general, reimbursement for psychologists and psychiatrists by insurance is pretty low, which is why they choose to be OON.

> Using fairhealthconsumer.org for DC and this billing code, the typical provider charges $230 (80th percentile of charges) and the typical plan will pay 70% of out of network charges or $161.

I don't think they'll budge on this because there's an allowed amount, similar to in-network, right? So let's say for a procedure the allowed amount is $1200. The insurance would pay 80% ($960) and you'd pay 20%. They're not going to suddenly cover 90%. It's pretty much the same thing.

For my previous employer insurance, for mental health, it was 90% INN and 80% OON.

You can search for HCPCS codes here (since all private insurance bases their reimbursement on Medicare, so if Medicare pays less, they pay less):
https://www.cms.gov/medicare/physician-fee-schedule/search?Y=0&T=4&HT=0&CT=3&H1=90834&M=5