Why don't you want to sister anything on? You don't have to go back the 12 feet. Anything is better than nothing. *I* would try to sister on what I could beyond both directions of the cut out by a couple feet perhaps. It helps to predrill and use galvanized screws. You also could bolt. You also could use a piece of 1/4 inch steel with holes predrilled through it, staggered as not not cause a split in the joist.
Also bear in mind that if you plywood correctly around the toilet, that you will want to span the cut-out joist with solid unbroken plywood, to reach the joists on each side of the cut out one, in one piece. This procedure alone will help carry some weight.
*IF* you have a toilet flange sticking up, that is, say, something you don't want to mess with, like cast? Then you really need to cut the plywood in half, with the cut going through the circle cut out, so that you can slip each half of plywood under the flange so you have the flange sitting on the plywood, as opposed to just encircling it. If you felt, due to the cut out, and the fact it is over the notched joist, that you would like to beef up this joint, if you cut the plywood in half,... you could prescrew on a piece of plywood on each side of the one piece of plywood floor to be slipped under the flange. Then after you install the second piece of floor plywood that you have cut in half , then screw through the plywood that was prescrewed onto the first piece.
I am a master all all these type of repairs as I have gutted out many bathroom floors and mobile home floors down to the joists and came across the very thing you speak of. Oh...and in cases where you want to sister on a longer board but can't figure how you can nail or screw under the existing floor?...it helps then to pre-nail the nails onto the sistered piece first, so that you can lay on your stomach and reach inside the joist cavity to hammer. And you can use the side of the hammer to nail with, also. Also, for extra bonding, you could use PL-200 sandwiched in there, as well.