Thanks to everyone. All of you make a lot of valid points, especially with regard to the physical demands required to do it with a hand sander. But I have no illusions that it will be quick or easy.
You also make a very compelling argument for renting and under different circumstances you might have talked me into it. But the reason why I'm reluctant to rent comes down to simple practical logistics. I live in a large city without a car and I'm not going to drag a large unwieldy sander several blocks onto a subway or bus then hump it several more blocks to my home every weekend. Then back again the next day.
Yes, I might be able to shoe-horn it into a cab or Über etc. but that doesn't sound much better and it's more $. Nor can I borrow my neighbor's car because like me they don't have one. Even if they did I couldn't realistically ask to use their car week after week. Nothing about renting is convenient or practical in this particular case. In fact, while I find the prospect of being hunched over a small sander unappealing it seems
far less exhausting than the weekly ordeal of pickup / return.
One thing working in my favor is that there's no hard finish (lacquer, varnish, shellac, poly etc.) that must be removed. Also the flooring is in good structural condition despite being more than a century old (a testament to that Old World craftsmanship as far as I'm concerned). Considering what the rest of the original woodwork looks like my guess is the flooring might have been oiled (or stained) at most. In any case I won't need to scrub through layers of finish nor do I need to remove every scratch or imperfection. It's an old house, it's part of the history and charm.
So while I completely agree the hand-sander route is far from ideal and sure to be physically demanding it's still the most realistic option. I imagine it will be similar to working in a garden hunched over for hours on end. The video
@guybo posted gives me some hope that it's doable with some hard work.
