I have a CC with a grill and it is relatively easy to clean and maintain. Before first use, I lined it with foil like in Trevor's video on his Eurostoves website.

With the exception of lining it with foil, I treat it like my outdoor grill. When I'm done grilling, I crank up the heat and let it carbonize the bits on the grate. I sometimes do this while I'm eating, especially if it's just a quick meal. Then, when it's done smoking and still hot, I use an outdoor grill brush with stainless steel bristles and give it a good brush, pushing bits and dust down. I also wipe up any grease in the grease catcher on the front of the grill rather than push the grease into the hole to the drip pan. Then I let it cool and put the cover back on. The next time I need it, I just remove the cover and turn it on. On one occasion I didn't clean it afterwards. As a result, I had to clean the grill with the above method before I used it. The process also served to preheat the grill but it also took longer to begin cooking.

I've used my range for about 10 months now and I have only done a full clean to it once about two months ago. I was kind of surprised that it was cleaner than I thought. After breaking it down, just wiped down the insides and used some BKF in a couple of spots. Then I replaced the foil. I also noticed that there wasn't a lot of grease in the drip tray. Just a few spots on the foil. Compare that to my Weber where the area below the burners is full of grease and grease saturated bits. I've had grease fires on the Weber, but never on the CC. My guess is that it's partly due to the design of the grates. The grates have channels/runnels that send the excess grease to the grease catcher in front. The ceramic racks underneath were just washed in the sink and air dried. Once I put it it all back togeher, I fired it up and let it smoke out before shutting it down and covering it again. I'm thinking that this full clean may only be a yearly thing for me. I think at a minimum I'll just inspect the foil going forward and clean it if necessary.

Trevor's video is fantastic and I wish Eurostove had a West Coast branch! Thanks for mentioning it!

Here's the video for anyone who stumbles across this thread in the future.
http://www.youtube.com/watch?v=1C0pgVqpECY

Here is a link that might be useful: Cleaning a Capital Culinarian grill

I opted to leave the burner in place when lining with foil. But I my try that next time.