How should I frame a small void in my floor system to support subfloor?
None of the ideas that you outlined are really ideal. Probably the best approach would be to cut some pieces of joist sized material (2 x 10s if I read your question properly) to be used as blocking between the open joist and the one down under that wall. These would be cut to match the spacing between those two joists. You can use metal joist hangers to secure them in place. I would space these equivalent to your normal joist spacing. 

This picture shows the idea where you would place these.



Another alternative is to use some joist sized material cut to length and just lay it up against the outer joist that is under that wall and simply screw it through the face into that covered joist. It may take several iterations of this to being out the top of these sistered joists so that the top extends beyond the wall surface. This alternative may be easier so as to avoid difficulty with the electrical wire running through that area unless the wire is already below the bottom of the existing joists.