Here we have something called the Standard Health Questionnaire (SHQ), which they make you fill out when applying for insurance. But there are a bunch of exceptions at the top which make it possible to avoid submitting the SHQ. Running out of COBRA is one of those exceptions.
This is exactly how it worked for me when my COBRA coverage expired and I lived in WA. Bypassing the SHQ was key to getting reasonable rates for myself.
