We moved into our house with a gas range in the kitchen island, no venting at all. For what it is worth, we are a sample size of 1, but we have had no issues at all. We cook a lot for a family of 7. (So of your 3 options, I choose #3)
But first, check out a new option - #4. Which would be what Tetsuya Hondo just posted. Or, when our control board died, the local repair company (before I read this blog I simply called them, how stupid!) told me it was the board and they could no longer buy the part. They were right, but I found a place to repair it:
http://www.fixyourboard.com/boards.html . We had to send it out for 1-2 weeks, for a flat fee of $160, but it worked awesome! It saved us the $1,000+ for a new stove. It has been running for about 1 year now since the repair.
Maybe you could try this, and look online to help with adding the insulation to prevent the problem again.
(I can't believe people buy $3,000 stoves with 1 year warranties . . . . . My stove is 10ish years old, but looks like new .... yet they don't make parts for it ..... crazy)
Edit: Spork, just read your entry below. I like your thinking, why does a stove need a control board .... I will look for antique when I need to replace.