I have a Morgan Out Island 30 with a similar keel configuration. It doesn't turn on a dime, but more like turning on a mint... the US Mint to be exact. All joking aside, I will throw something out there, but please take it with a grain of salt, we've only had our boat for the last half of last summer.
Are you getting decent backing speed? We have had trouble shifting in and out of gears, a problem I haven't tracked down yet (I'm going to look into a stretched cable...). Last summer, we would shift into forward, and it would go forward, but not very quickly. The engine would be revving high, and we wouldn't be going anywhere fast. We'd have to throttle back, put it in neutral and try again.
My point is that you may not be fully engaging the prop in reverse, so you are getting spin, causing some prop walk, but aren't getting the backing speed quickly enough to get steerage. Just an idea to muddy up the waters
P.S. We have a three-blade prop as well (16 x 10) and a 2QM20. We haven't really had any trouble backing, once we can get it to engage. We can easily make 6.5 knots forward.