I am wondering if the film is something on the floor or just signs of wear. It sounds like you have tried a polish but if you haven't, you might just spray a small area with Pledge and wipe it off. If that doesn't work you can still use the Pledge on furniture. That reminds me of an old home remedy for bringing new life to furniture wood. Just mix equal parts of Vinegar, Turpentine, and Raw Linseed Oil in a bottle by shaking. Pour some on a rag and rub the surface. The vinegar and turpentine cut the film and the oil protects the finish. Then wipe with a clean rag.

My trick is while your damp mopping, have a towel under your feet to dry as you go. I always ended up with streaks or a film even the recommended Bona or whatever it was called.

I had that problem too, I had quite a biuld up that took several moppings with vinegar to remove. I switched to a steam mop and it made a big difference for me, no more build up. I just used vinegar, nothing else.

The steam mop or the vinegar? I've never had any problems with the steam mop, the vinegar I used only when I was getting rid of the buildup, and not since.

eta your question made me curious so I did a little research and apparently you shouldn't use a steam mop as it could affect the adhesive. Wish I had researched that about 5 years earlier, lol. I have been using a steam mop once a week for 5 years with great results, but I can't recommend it knowing what I know now.