How important is changing the battery on an HRM?
 

I'm trying to decide between getting the Polar F6 and F11 and it seems like the big selling point on the F11 is that I can change the battery. Is a changeable (probably not a word) battery really worth the extra $50?

I don't think so. I've had a number of Polars, and the batteries in the chest strap last years. Then you can either buy a new HRM or belt for the $50.

Is it possible to just send Polar the transmitter and have them replace it? That would be better/cheaper than buying a new strap.

You're going to want to be able to change it yourself. Inevitably it will go out when you need it.
I don't buy watches, hrms, dive computers, etc where I can't change the batteries myself.
Most of those hrm belt batteries last 1-2 years.

Sigma cyclometers with HRM allow you to change the battery yourself. Also, if you are going wireless, look for an HRM that sends the information in digital packets rather than as an analog signal. The digital variety are immune to interference from stray electrical signals.

I have an inexpensive MIO watch with HRM. I have learned how to relax my left arm while touching the buttons with my right hand fingers. I can continue to pedal at the same intensity while waiting for a reading. It works pretty well because most of the time I am trying to hold my HR in a general area, not within 5 points one way or the other.

Good news! "Changeable" is a word, according to my spell checker.