JB...so what you're saying is...leave the gym finish there and go over the top with a 'duller' sheen product (lightly sanding first?)
That sounds like a plan to me but I have no way of knowing what was used on this floor the first go-around other than the previous owner did know that her husband used a gym finish. There are no containers left and he isn't around either.
And I do agree with both of you that the gym finish is hard...this floor was refinished some 10+ years ago and it looks great. Especially for a high-traffic area. The finish has held it's ground firmly!