Didn't you get a choice of which plan? My last company I worked with (3 years ago) had 3 "choices". Odd an insurance company wouldn't give their employees options!
I understand the wanting to pay more for piece of mind

I'm that way too. Fortunately I have my husband for peace of mind, knowing if I get sick he'll make sure I'm taken care of/knows how to take care of me well.
Can you save a bit of extra money each month in case you do get sick (until you have at least a $3,000 cushion)? That's what I would try to do. I've only had an HMO once, back in the 1970's/1980's when they were a "new" idea and had to compete with the old plans so were really good AND cheap. But back then (before the HMO though) when I was in therapy, it was ALL covered and I was paying like $12 a session twice a week, for the entire year/as much as I needed. Those were the days! Don't think we'll see that again. I saved my budget books from then; didn't have much income and it was a struggle but looks so good now. . .