I've not been up Mt Whitney (!) but I often bacpack in mountains and wild country with camera gear. My advice is, be ruthless. Think what you absolutely need to get by, rather than what would be nice to have.
Think carefully about clothes - ideally use lightweight outdoor stuff that you can wash and dry easily - and take just one change. Same goes for food and cooking gear - can you get by with a small number of utensils? Can you use lots of dry food to rehydrate, or even food you don't need to heat? Think dried fruit, flapjacks. And remember water - it's often a killer in terms of weight. It's dead important too, so that means you need to save weight ewlsewhere as much as possible.
Gear-wise, be selective. I use a Pentax 67II kit with x5 lenses for much of my landscape work. I also use a Fotoman 617II. But if I'm on a backpacking / mountain trip I use my much lighter and compact Fuji GA645zi and a much much lighter tripod than normal. I stabilise this with a long climbing sling which I loop round the tripod and then stand on for extra rigidity. When backpacking, everything is a weight trade-off...!
Your legs and back will thank you for being ruthless, and you will have a much more enjoyable trip if you're not constantly fighting your kit. And I'd advise a bit of training too.
Have fun - post some of your photos from the trip to the APUG gallery.
Hope this helps,
PS- You might find the APUG 'Hiking and Trekking' group interesting?