My rule of thumb is that you want to stay above and away from 220 as that's when the effects of balance poise errors get flipped and magnified. Your movement dipping in and out of 220 isn't doing it any favors in terms of positional consistency.
Hmm, that's what was in there? What's the movement diameter? 0.12 is still pretty strong for anything I'd call a "ladies" movement. For example a Peseux 7001, at 10.5"' takes a 0.11 or 0.12 depending where you look, but at 21,600 does need a bit more power. A typical 10"' LeCoultre from the same period as your patek takes a 0.10 or sometimes even thinner. These are what would be considered smaller mens movements.
On edit- Ah, ok, you actually have a barrel with a 9mm inside diameter? Ok that's not what would typically be called a ladies movement even if in a ladies watch. The one you just posted coud work but it's anyone's guess if the T from a Waltham spring lines up.