Welcome, Nick. Please go to the UserCP above, find Edit Signature, and enter your first name there so it will appear in each post for us and we won't hafta search for it, eh?
While oak is a strong wood, it's not particularly rigid. In your situation I would leave it in place, though. I suggest you might wanna increase your top layer to 5/8ths ply, AC or BC or whatever is readily available.
And for sure you wanna go through there and add some decking screws in the existing boards. I recommend pre-drilling the boards. Old wood flooring was notoriously loose in the fastening.
Do you know what material those joists are? And do you know the actual unsupported span?
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I've heard the wood they used back then is much better in terms of strength.
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Not always true and accurate.
Not very worthwhile to try to actually measure the joist deflection unless you are capable of loading the entire floor to at least 40 psf. If you can determine the wood specie, you may find the design deflection is within spec if those joists are a full 2 by 6 inches. Presuming the span to actually be ten feet.
And if that span is accurate, you'd want a deflection in the center of not more than a third of an inch, fully loaded. That's L (length in inches) divided by 360. But measuring it accurately and correctly ain't a simple proposition.
My opinion; worth price charged.
