Goodness, you have lots to digest after a Chiari diagnosis. I hope that you find some answers both here and through your doctors.
In regards to life insurance, you will probably not qualify as you have a diagnosis of Chiari, have symptoms, and surgery has been suggested. An insurance company will not offer coverage to you until one year after surgery and that is if you do not have symptoms. If you do have symptoms (other than a headache) they will charge you more or disallow you. This has been my case anyways.
My opinion on surgery is the soon the better after a diagnosis if your health can support it. The brain does not always bounce back from continuous pressure. Just my thought with no basis on scientific knowledge!
In regards to your symptoms, I have always thought of Chiari as have a two tiered system of symptoms. Headache, numbness, muscle weakness (with others too!) on the first tier. This first tier the doctors typically understand, can fit into their knowledge base of Chiari, and can often measure.
The second tier becomes more variable between clients and includes what you listed above - brain fog, body twitches, memory loss, vision changes. I would put the swallowing difficulties in the first tier. This second tier seems to cause the most problems in terms of dealing with medical professionals as there does not appear to be a direct neurological or anatomical reason to explain all these funny symptoms. Nor do doctors have much to offer to alleviate symptoms. This is no doubt why Chiari clients often get painted with the crazy brush!
My understanding from talking with medical folk is that these second tier symptoms are not necessarily specific to Chiari but are shared by people under neurological stress (MS, dementia, tumors, brain injuries...). The brain becomes over-stressed and some areas start to underperform. Reasearch people are starting to identify frontal release signs or re-emerging primitive reflexes as contributing to these symptoms. We, as Chiari folk, experience this as vision problems, fatigue, temperature regulation, and balance issues.
I guess that in a way your doctor is right that Chiari is only causing the headache/numbness as that fits within his knowledge base and understanding of Chiari from what he learned in school.
From my reading, surgery does a better job of correcting the first tier of symptoms but less so with the second. I found that exercises to extinguish primitive reflexes have helped with some of those. I have yet to master the fatigue issue but I keep hoping!
Good luck, again, in finding the information you need to relax with your diagnosis and the scariness surgery can seem to be