The best way to cover the patch is to pull up the floorboards as you described. Use the old boards as much as you can and make certain that the joints are staggered when you lay them back down. You may have to cut or chisel off the bottom piece of the grooved edge in order to fit the boards back in. Make certain that the boards are parallel.
A big issue is what are you going to use for additional flooring that you will need? The ideal solution would be to steal some flooring from other portions of the house that may be carpeted or covered with linoleum or other flooring. Perhaps there are flooring scraps in the attic, but that's a longshot. It is very difficult to get the new boards to match. Even if they match the color -- which is a good trick in itself -- the grain of the wood will not match. I would try to buy some old flooring that is the same wood type and size and approximately the same age as your flooring, but this will take some searching.
Some people like to the "weave" the replacement boards in with the original boards but I don't like this because they always stand out like a sore thumb. A better approach is to use up the original boards first and then use replacement boards to finish the edge of the room. This way, there is only one transition area between the old and new boards and you may be able to cover much of this with a carpet or couch. Don't put the new boards in the middle of the room!
Practice matching the stains using scraps of the old and new boards until you get it right before applying any stain to the sanded floor.