I'm pretty sure that a 'military-person' can bring their vehicle to ca, and continue to operate it using their 'home-state' registration. You might try looking up the rules in the ca vehicle code, found at www.dmv.ca.gov/dmv.htm#DMVHomepage
If you can keep your 'home' registration, you will not have to deal with emissions testing.
If you have to register in ca, you will be faced with having all of the original emissions devices in-place, and working. (No 'cost-limits' on this, you just have to replace all of the original stuff.) And, you will be faced with a smog inspection at the initial registration, then every two-years.
On the web page, you will find a place to click for 'field offices'. You might try one of the 'non-big-city' offices, where you can talk to a real person, and call them, and ask your questions. I suggest places like Jackson, or Placerville.
CJDave might offer an opinion, here, as I believe he is dealing with a 'non-ca' Jeep that has had the emissions stuff removed.
Getting and installing the emissions stuff should not be too big a deal.
But, hope that you can keep going with your Alaska registration. If you are only on a 'couple-year' assignment, I'd bet you could do the time without anyone even noticing. The thing that might be noticable, and often catches people, is using the vehicle day-in and day-out, travelling the same route, at 'going-to-work', and 'going-home' time. I live in a little town, where this is the case. But, no problem... it's not very hard to 'skirt' around this town.
Best of luck.