Hi. Here's a couple few things you can try at home (with gear setup)
(1) Try increasing your ISO and reducing your flash power and see if this reduces the number of shots with the shutter showing. Flash strength is proportional to duration so half strength will be roughly twice as fast and therefore allow a bit more latitude for the full flash while the shutter is open. Flash duration is very small but at full power on a small strobe I'm not sure it is as short as the conventional wisdom would lead us to believe.
(2) I read on a post here that someone noticed that the frequency of shutter appearing was different between landscape and portrait shots. As the shutter is mechanical a bit of gravity (in the right direction) may possibly help.
(3) I've also read that hard wiring with sync cords gives better sync speeds than FO but I haven't seen anything that really explains why. And that also doesn't explain the difference between your YS110 and D1.
Hope that helps.