Does anyone know of a source that helps get reluctant insurance companies pay up on long-term medical insurance claims?

File a complaint with your state insurance commissioner. They'll get on them.

Each State has a Department of Insurance Regulations.
In Virginia it is the SCC : State Corporation Commission

Contact the agent or group who sold you the policy. My husband bought our policy thru his retiree union. After my accident, I called the union and they sent me the forms for my doctor to complete. I sent to the union office and they got it filed and payments started. My check is paid directly to my checking account each month.

A lawyer?

You might post this at www.Bogleheads.org.

Great financial advice and lots of folks who are knowledgeable about insurance.