treating rotten wood
I suggest you try a lumber outfit in your area that does pressure treating, if there is one. See what they can do for you.
The bottom line here is that you aren't going to be able to get anything that's 'paintable' that will work with any sort of reliability. And as mentioned by rpxlpx, you certainly aren't going to be able to purchase chemicals that we use to commercially treat lumber. If the place that he mentioned earlier ever sold CCA to Joe Average, they'd be in a whole lot of trouble. CCA and the new copper variants (CA-B, ACQ, and others) are all federally-regulated chemicals that can only be possessed and applied by licensed pesticide applicators.
That said, you're going to end up having to either replace the entire timber, or remove the rotted part and pour a pillar footing or some similar support. Rotted wood is structurally compromised to start out with, and there's nothing you or even we could do to retreat that timber back to the point where it's fit for use. In the long run, encasing a rotting timber in concrete is asking for trouble, no matter how much rot is there.
If you're replacing the entire timber with a CCA-treated one, you're going to want to look for .60 pcf treated lumber. .60 pcf is a greater retention than run of the mill .40 pcf lumber, and will give you added protection.
If you're going to replace the entire timber with one of the new copper variants, such as Copper Azole, then you're going to want to look for material treated with a Ground Contact spec.
The treated lumber industry will move entirely to copper variants and cease to manufacture CCA by December of this year. Both are available on the open market at this point, so look for the above mentioned specs for each respective chemical.
I guess the point is here that there is no retail-level field dressing material that I feel will be able to perform what you're asking. I'd replace the entire timber or cut off the bad material and pour a column to support the good length