I do not practice in Missouri, but each state has different insurance laws that require a response to your demand. Generally, however, this only applies to your own insurance company. If they have not responded to you within 30 days, I would write and call the adjusters supervisor and speak with them. Always follow up with a letter as you want everything in writing. Depending on the amount of your demand, you may file in small claims or seek the assistance of an attorney experienced in these matters. Often, the adjuster will change one an attorney has agreed to represent you. Good luck and keep at it.
Having handled thousands of personal injury settlements in Massachusetts and New Hampshire in the last 20 years, I know one thing - you will need an attorney to assist you in presenting and optimizing a claim.
I want to answer you question. But, getting a time frame on a settlement in general is like asking "How long does it take to fix a car?". Is it an oil change or rebuilding the engine?