I don't see any reason why PT wood of the same size would not be a good decision. Carriage bolts, lag bolts or a series of durable screws could be used as the fasteners. Make sure that whatever you use is either zinc coated or galvanized to reduce deterioration.
In order for sistering to be effective, you need to encorporate an equal distance on either side of the defective joists for the new attached lumber. The longer the stronger. On this situation I would suggest a good 4 foot on each side. So that would be a 8 foot long board.
Now, the true sistering term only goes as far as securing a broken board and applying a new board to the old board as to carry on the load of the first. If the original or defective board goes into the foundation some way then this opens up a completely new project.
The way I see it now is that you don't have a good part on the opposite end of the defective board for the sister board to attach to, therefore, sistering would not be the answer.
Sounds like you need to chisel our or remove the old joists from the foundation attaching point and add a new board there. Then carry this new board to the old joists. You will need to saw off a clean section of the old joists for the new joists to join up to. Now with the new joists in the old joists position and butted up to the original joist, NOW you can do the sistering part.
If this is all out of whack, then I do not fully understand the original question.
I am trying to see this in my mind without seeing it with my eyes. Sometimes these projects are hard to envision.