It's not likely that the boards on either side of the removed partition will line up. Unless you're fine with installing short filler pieces, it would be best to remove floor back to the line where the voids end, remove the nails, reinstall the floor and add new wood at the edge as needed. It's more labor to do this but will use less wood and maintain the integrity of the tongues and grooves.
Old wood is often laid using big cut nails and can be removed without damage if done carefully. You might have to sacrifice a row of wood to get access to the tongue edge of the board.
If the floor was initially laid from the left side of the picture to the right, you should use a spline/slip tongue to change the direction. If it was laid right to left you're good to go.
At a minimum you can also add a layer of building paper. Laying the new wood at the edge allows you to doctor up the finish more easily to make it match the old (if needed), avoids the necessity to match the exact t&g profile and allows you to use a slightly different width which might save you money.

Thanks for the advice! We just discussed it, and it looks like we're going to go ahead and replace it with new pine floor given the missing patches and trouble it'll be to make it all line up.

If the flooring is original, you might be able to remove it and sell it to someone who's doing a renovation. At the very least it might pay off to see if it's worth doing in your area. Salvaged Yellow Pine can sell for quite a premium to new. I have offered to tear up people's floors for free even if I didn't get the job to put their new floor down. I can sell it for a decent amount and get a leg up on my competition to generate a floor refinishing job.

With your chosen path you will get a more flawless floor without the big gaps and it will all be tight so it's not a bad idea. It's probably not hard to tear that floor up but you would have to clean all the crud off the edges to get it to fit up tight.
Good luck!