Distilled water doesn't have enough minerals to bring out subtle flavors. Many good water purification systems have a re-mineralization filter, usually of volcanic rock. For instance, I use a counter-top Santevia system, and in the water chamber I put this rock and it really helps. The ceramic balls in this mix don't seem to help much, but the rocks themselves make a huge difference.
I used to use one before upgrading to a larger countertop filter system. I found the taste to be a little less flat than purified water, and with our tap water it was about the same as spring water. The countertop system I use has a re-mineralization layer with volcanic porphys rock and I find that beats most spring water and makes subtle tea notes "pop." Theoretically you could add some of these rocks to the bottom chamber of your Brita for a similar effect (you can buy the rocks separately), but the rocks clanking around while you pour might be an annoyance.
I'm curious - is there a reason why you are adding the rice to your kettle rather than to your teapot? I'd think it would require a good washing out of your teapot with some frequency.
That said, if you're into experimenting with adding things to your water, have you tried re-mineralizing it with volcanic porphys stones? Some water filters have them, and they sell then separately to sit in your water tank. One tea shop I know even keeps them in their glass kettle, but I find it adds way too much mineralization to the water if you do that. When added to cold water storage it adds just enough minerals that subtle tea flavors really "pop" -- I've been doing it for years now with some in the bottom of my countertop water filtration system.
I got the maifan stones from the same company that sold the Santevia water filtration system (they sell them specifically for re-mineralization use, plus they have a layer of maifan stones on some of their 7-layer filters). The kind they're seling now on Amazon also has some ceramic balls, but those are easily removed if you aren't using the maifan stones with cold water.
As for the Kamjoves, I've had a dozen over the years. Some were re-wired for American 110v currents rather than being designed for it, and those tended to konk out after a year or two (in once case the wires inside melted!), but the better ones have been workhorses.
My best Kamjove experience is a Chinese market 220v kettle that was gifted to us by a Fujian tea company at the World Tea Expo -- we bought a step-up/step-down portable transformer from Amazon for about $80 so we could us it on our 110v outlets and the thing boils water is less than half the time of any of our other kettles!
I've had both induction Kamjoves and the kind that set over a ring spring connector plate. The induction kinds are nifty but don't really seem to have much advantage over the "normal" kind. I have a neat one that's like a figure-eight, with one induction plate for a kettle and one inset induction plate for a cup sterilizer chamber. Our favorite tea shop, Spring Cottage Tea House in Richmond B.C. has just imported a funky Kamjove set that has a normal kettle but also a tea water spigot for refilling that links to a water bottle you keep under the table (I think he plans on selling them for about $80 CDN, or $65 USD at current exchange rates).
I find my Kamjoves everywhere in Chinese tea shops, and just about every Chinese herbal shop as well. I really never see them outside these two kinds of stores though.
Yup. Your well water probably has a higher mineral content than the Brita water. If you're used to the well water the filtered water tea can come across as flat. A bit surprising that it would mute such a strong taste as bergamot though.
If you have the option, you may want to look into adding some mineral content simply by tossing into the bottom of the Brita pitcher a few volcanic rocks of the kind used in filters that re-mineralize the water. This is the type you need (well, minus the ceramic spheres) but you should be able to find them elsewhere cheaper: http://www.amazon.com/Santevia-Mineral-Stone-Post-Filter-Filter/dp/B003T46666/ref=sr_1_22?ie=UTF8&qid=1341956550&sr=8-22&keywords=santevia+water.
BTW: I have a Santevia system despite having excellent Pacific Northwest mountain range tap water, and it does wonders to improve quite a few of my teas. Expensive, but worthwhile if you really want better water for your tea.