Alan Chenkin, Lifelong Carpenter/Cabinetmaker, owned an AWI certified shop for 10 years.
With fine sandpaper you can even-out the finish, without going all the way down to the bare wood. You can also apply a layer of finish over the sanded area I would test an inconspicuous place (inside a closet, as an example) with 120 or 150 grit sandpaper, using an orbital sander. Use a 1/2 sheet sander like this
Makita BO4900V 2.9 Amp Variable Speed 1/2 Sheet Sander with Paper Dust Bag – Power Sheet Sanders – Amazon.com.
Belt sanders are very aggressive, and these orbital sanders are more forgiving. This is especially true when sanding wood with a very noticeable grain. If the existing finish is not worn out, you can use fine grit #220 sandpaper to scuff it so it will take a new finish well. If you have to take more of the finish off, start with the coarser #100 or #120 grit sandpaper to remove any heavy scratches.
I once sanded an entire 8×10 room with two of these, a lot of fresh sandpaper, some serious dust masks, and lots of patience. Not always the best way, but it worked – even though my hands vibrated on their own for almost 2 days afterwards!
If the test worked out, consider renting a large pad sander. Please wear dust protection, exhaust the dust with a window fan, and keep a shop vac handy to pick up the dust. Be careful when you clean the gaps, as floors do move – and will compress and expand any filler you apply.
The Do-It-Yourself Guide To Hardwood Flooring: Everything You Need To Know To Install, Sand, And Finish Hardwood Flooring: Chip Alliman: 9781442107908: Amazon.com: Books
Best of luck with your project! – Alan