Everyone here is right about the potential of an El Nino year -- if it is, it'll be a little more of a thrash. Crampons & ice ax (maybe -- you'd have to know how to use one; otherwise ski poles) for Harrison and you might want to avoid Pants Pass.
Also, if your trip originates in Sequoia Kings (Cedar Grove) you don't need a separate permit for Whitney -- if you originate from a USFS trailhead, you do. I'm not 100% sure, but I think you're allowed to go out for a 24 hour resupply on the Whitney trail and back in (or, alternatively, out there and back in Cottonwood to fish Sky Blue).
To a certain extent, you're going to have to be flexible to see what snow conditions are going to be and adjust your trip accordingly. The main trails would be OK, but the cross country passes might be a problem.
Although not approved in all wilderness areas I like to use a bear bag tied to a solid object or hung in a tree. There is allot of controversy with that but I have never had a problem with a bear even trying for my food and I have had them come through my camp.
No controversy. If you're in an area where canisters are required, you can't use the Ursack (I think that's what you mean by bear bag??) tied to a solid object or even counter balanced. Everything in the Bubbs Creek drainage requires canisters or use the boxes. When you go over into the Kern drainage, you can use the Ursack, but only as a counter-balancing bag -- not tied out to a tree or whatever. The Ursack is not allowed to be used (as they intend it) in Sequoia Kings. You can use it as a regular counter-balance bag, though.