If HR can’t help and you can’t get private insurance, remember you can pay out of pocket. If you’re paying out of pocket, ask about cash deals upfront. Use GoodRX app for prescription coupons. I paid $300 through insurance for a prescription that I later found out was $150 out of pocket at the same place (Walgreens pharmacy) with the GoodRX coupon. So stupid. I also learned that visits to CVS Minute clinic, with basic testing, only costs like $70 when even my old insurance charged a ~$25 co-pay (not much of a discount ), and that I once paid a $10 prescription co-pay for antibiotics that were actually only ~$1 out of pocket. So while it’s risky to not have catastrophic coverage, in general it’s more affordable to pay out of pocket for common visits and issues than you would think. Because insurance costs jack up prices. I’m not recommending you skip insurance, just hoping to provide some reassurance if things don’t work out in your attempts to get insured before December.
Also, not sure the age of your kid but if it’s a college student, universities usually offer student health insurance.