Hi Chunky. While I have had some experience with a wedge on both an 8" LX200 (portable) and a 10" LX200 (pier), its been a while. I've since decided (a few years ago now) that an eq mount is for me. That doesn't mean that the wedge didn't work, I did find it fiddly at first to learn. I also found it did take me some time to setup accurate when I wanted to travel away from home.
If you can learn to drift align, especially using a webcam and software (I'm a K3CCDTools fan for this) the polar alignment of the wedge isn't a major drama. In fact the basics are no difference than for an eq mount.
One thing I did experience being wedge mounted was significant damping down times, and the setup had very little tolerance of disturbances, hanging and dragging wires mainly, but even light gusts of wind could disturb the mount significantly when imaging. I imagine with a 12" the problems would be amplified. However I know of at least one IIS member (thunderchildobs) who had a wedge mounted 12" doing supernova surveying.
I found the biggest issue with polar aligning the LX200 with a wedge was not the wedge itself, but the painful alignment process needed for the Autostar. Not intuitive, not straight forward (well that just describes the whole software to a T for me
) and I believe, a real challenge for many inexperienced astronomers to identify sigma octans in a finderscope, let alone an eyepiece. Fortunately there are work arounds available.