I have old (110 years) pine floors with tinted shellac on about 4 feet of the perimeter of each room, leaving a large unfinished square in the center of each room. Will I ever be able to refinish them so that they will be somewhat uniform in tone?
You will probably have to sand what's left of the shellac down to the wood, then find a stain you like. But remember to sand the rest of the floor as well.
The previous owner of my old house started sanding the master bedroom, then up and died, leaving the floor only about 3/4 sanded. When we moved in, I expected to carpet eventually, so I just tossed a rug over it. A few months ago, I emptied the room, and hand sanded what the previous owner had missed. I noticed there was a lot of ground in dirt, so I sanded the bare wood too.
Then I used a wood conditioner over all of it, stained, and now the whole floor matches quite well - not perfectly, but well enough that the difference isn't noticeable with furniture in the room.
Since it's an old house, and the floors are original, they have a lot of character. I like them the way they look with just a little Murphy's oil soap.
Give it a try - the worst that could happen is you'd cover them with carpet!