Vapor barrier, in most cold climates, (and I note that because you're in CA, which is different from the very cold upstate NY which I am familiar with) is on the warm side of the wall, not on the exterior.

Vapor barrier is there to hold house moisture INSIDE the house, away from the insulation, not to exclue exterior moisture. If you're exposing the studs you can apply a vapor barrier, after you insulate, before you plaster or hang sheetrock. The fiberglass with the heavy kraft paper backing will function, somewhat, as a vapor barrier, but if you've got your whole walls open, it's easy to install a proper one at that time.

Now, you may also be concerned about moisture penetration from the outside, chiefly driven rain. That's where those house wraps are employed, but those are not "vapor barriers", in the same meaning, since they are not excluding air-borne moisture vapor as much as liquid precipitation. I can see no way to install one w/o pulling your siding which you may not be interested in doing. I think a good paint job, with well-maintained caulking, and perhaps wall and soffit vents would be satisfactory substitutes for house wrap. Are you sure you don't have any sheathing in the exterior cladding? You may have tar paper between the layers.

The (in)famous old house problem with non vapor-barriered insulation is primarily one where moisture migreates outward into the insulation from the house, then condenses inside the insulation (particularly other kinds than fiberglass) causing problems. Depending on your climate it may not be such a big deal as it is in very long season, frigid areas.

HTH
Molly~

in)famous old house problem with non vapor-barriered insulation is primarily one where moisture migreates outward into the insulation from the house, then condenses inside the insulation

Moisture damaged insulation has soared since Building Codes started mandating tightly-fitting polyethylene vapour barriers on the interior side of the drywall. While the poly reduces moisture travel from interior to exterior in winter, it traps water vapour moving the other way in the summer. As building Science Corporation research demonstrates, the wall assemblies that perform best in both conditions are designed with an eye to the climate they're operating in.

Once you know exactly how your home is constructed, you can consider your design. As with housekeeping, I think there's likely something behind the exterior cladding. Personally, I would go with an insulation that is not affected by moisture--ruling out batts--and possibly a vapour retarder, as you are considering.

Try to look at the Building Science material. It is top of its class with no commerical axe to grind.

Here is a link that might be useful: Building Science Corporation

We would need to know what the climate is in Eureka, CA. It's a very big state. We would also need to know if you intend to air condition the house.

The home is in Eureka, located in Northern California, about twenty blocks from the ocean. Temperature ranges between 30 degrees during winter to 75 degrees during summer. There is no need to air condition the home.

Eureka is in marine a region, a new category which BSC doesn't offer details on. I think their suggestions for construction in "mixed" zones would be helpful.

In my climate (which is a cooling climate)
the balloon framing is an issue.
if the wall is open @ the bottom of the wall
air will move in these cavities even when
insulated, and will reduce the R-value of
the insulation.

I am not familiar with Reflectix (which is a 1/4" thick, moisture proof, and supposedly has a 14.5 R Value)
but seriously doubt any 1/4" product has an R-value of 14.5
We see a lot of products that promise high R-values
and some do work, but only in specific applications.
Most require an air space between the reflective surface
and insulation or cladding.

btw Building Science has new info for costal
climates that may apply to your area in part.
best of luck