removing badly mottled varnish on oak floors

My wife and I recently bought a fixer-upper house built in 1954 and the oak hardwood floors need some help but I'm not sure exactly what to do.
There was wall-to-wall carpet in the living room, dining room, stairs, hall and master bedroom which had been down for at least 30-35 years judging by the condition of the padding under the carpet.
The finish isn't worn away, it has most of the same characteristics of the rest of the floor but is a mottled darker shade of reddish-gold. I suspect it's an effect of years of pressure and heat on the varnish itself; before we took up the carpet you could see where the previous owner had positioned and left his furniture for the past three decades, and this mottling appears only in what would have been high-traffic zones - around furniture, in the hallway, across the living room to the stairs, etc. This mottling isn't on top of the finish because it's not affected by any of the standard wood floor cleaners.
I really don't have the time at this point to sand the finish off and redo the floors. Is there something I can do short of sanding and refinishing the floors?
Thanks!
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snipped-for-privacy@gmail.com wrote:

Not really. You can try screening the floors (a screen is put on the bottom of a floor polisher which essentially is a mild sanding that doesn't remove much of the finish). Unfortunately that probably won't work. The mottling you're seeing has probably penetrated into the finish and will require sanding to remove it.
R
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wrote:

There are a variety of "Finish restoring" products for wood, floors and furnature that you might try. I forget the one I saw on TV but it looked like it might just actually be a watered down polyeurethane.
Try some thorough cleanings first to reduce the contrast to the traffic areas.
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wrote:

yellowed the old varnish . I did one sanding and wiped the floor with mineral spirits and this showed me it had helped but not got rid of all of it so I sanded again. Third time got it all. You could sand a small spot and refinish to see if this helps.
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snipped-for-privacy@gmail.com wrote:

Nothing other than putting down rugs.
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dadiOH
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Use Orange Glo Floor cleaner and refinishing kit You'll love it.
snipped-for-privacy@gmail.com wrote:

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