I happen to have a little training in Hungarian and Ukrainian style sabre fighting. There are movements from Western Europe (positions, blocks, cuts) but because of open grip and no finger ring there is a room for variety of wrist flicks, tricks, and hand switching that significantly help during one-on-one dueling and melee siege.
About difficulty to stop movement of a shamshir-there is another view. You don't stop the movement. You redirect it. It goes in circular motion all the time. Sabre should live together with a warrior's body. In time of training when I did about 1000 cuts and few hundred combinations in 2 hours I felt that body adjusts to this type of movement. It started working like one mechanism to save muscule energy for long time of battle. And this is an advantage of shamshir style. Plus i think, everyone will agree, that curved blade has much more cutting power then staight one. Open grip, no finger hook and strong curvature from my point of view are much better options for a big battles then straight blade closed grip and finger hold that suites better for smaller size dueling style European fights.
But don't forget great thing that Polish did - they put their techniques on paper for future reference.
But it is just my point of view