I play a 1984 Baldwin L (6 feet 3 inches) bought new, and I give the piano moderate use. Most tuner/technician/rebuilders advise that if a piano has regular use it's best to restring every 25 years or so. When you restring, the old #1 tuning pins are tossed out and larger #2 pins take their place. You might like the chrome plated ones rather than the blue steel variety for looks. Either will be snug in the pinblock. I had the Baldwin restrung in 2007. For the wound bass strings we used Arledge Bass Strings and for the steel strings Mapes International Gold musical wire. I instantly liked the sound better than the original strings.
The Steinway O built today likely has differences in design than your 1916 model, so you'd need to put the piano in very skilled hands. For an old piano, you should also be thinking about new hammers, shanks and flanges as well. If you consider keeping the original shanks, it's is a false economy as the old ones tend to be more brittle and breakable. New is better.
For the Baldwin it took about a year to attain tuning stability, but once it took, it was OK. The stretching of the strings especially occurs where the strings bend around the tuning pins, the bridge guide pins, and the terminal hitch pins. During the process I used my own tuning lever to take the curse of a unison or to pull up a low bass string here or there. Now I have the piano tuned four times a year, as I do recordings and I also live in a very challenging climate.
Before the Baldwin I owned a 1924 Steinway M. I bring this up to make a point. That is, if it turns out that the piano truly needs more than you thought and if the expense will rise significantly, then you have to deliberate on your options.
"Interpreting music means exploring the promise of the potential of possibilities." David April