First off devices with hard drives cannot be depended on at altitudes of 10,000 feet or greater (the base camp is at about 17,000 or so on both the Chinese/Tibet side and Nepalese side. The air is enough thinner that the spinning platters do not generate enough "airlift" to keep the head off the delicate platter surface. So I would forget those.
I'd go with plenty of cards, good media cases, and keep track of it all.
Here is a link to a couple that made the trip, they allowed me to present the images from this link to our local photo club, I got email permission and all they asked was that I credit them and their website. The offer some very good tips concerning spare batteries (fees for charging device batteries are pretty high at stops along the way).
http://theplanetd.com/everest-base-camp-adventure-the-arrival/I would start stocking up on SanDisk (don't chance anything lesser) Extreme Class (10) or even Extreme Pro UHS-1 (waterproof, temperature proof, shockproof, steel case etc.) 16GB or 32GB cards. I would order Pelican media cases (waterproof) and clip that to your backpack or camera bag with a strong lanyard. Mine hold 8 SDHC cards or the one for CF media holds 4. (Design has changed, current version holds 12 SD/SDHC cards) $19.29 at B&H.
http://www.bhphotovideo.com/c/product/828755-REG/Pelican_0910_015_110_0915_Memory_Card_Case.htmlDave 'n Deb took a Panasonic GH1 (he now shoots with a 5D MkII) and had no problems, The weather sealing on the 7D and L series lenses is a desirable feature but it's a heavy beast and the 17-40mm f2.8L might need it's own "porter". The f4L version might be bearable but remember you're going uphill for most of the time. See all of Dave 'n Debs shots for an idea of the trek on the Nepal side (most picturesque side, too). I believe I would go with a T3i or 60D and pack several Ziplock bags for moisture protection (but I believe your chances of rain are slim at that altitude). The 18-55mm "kit" lens (even on the 60D) would be my choice for it's light weight.
If you go with the T3i (or T2i) I'd carry two (once in a lifetime trip deserves backup), and I've had good luck with Opteka batteries ordered from amazon.com (lp-e8) listed as low as $9.95. I get the same life and performance as the Canon battery and they indicate charge left. I'd carry 10 to 20.
http://www.amazon.com/Opteka-LP-E8-2000mAh-Capacity-Battery/dp/B003LZ5SM6/ref=sr_1_9?ie=UTF8&qid=1326766744&sr=8-9For the 7D or 60D I'd go with the Genuine Canon battery or order a few from lacoloronline and test them out. Taky Cheung backs his stuff up to the hilt.
Carry all spare batteries in individual small ziplock bags (prevent short) and keep them in inside clothing pockets to keep them warm and keep them in your sleeping bag at night.
Hope this info helps you. But do check Dave 'n Deb's website and the link I gave. Invaluable info there.
Which side are you going with, China/Tibet or Nepal?