Did you check the details of the telescope aperture and focal length and the FOV? I had made an error, and when I corrected this, the process worked and rather fast (10 seconds for each solve).
The fov I put it at 0 and let a capture and solve fill it. And the solve works fine with the legacy polar alignment, but not the new one. Although to be 100% I was pretty far away from the pole as I don't have access to it from the terrace.
It doesn't need much sky at all. All the images it takes are going to be within the field of view of your mount's polarscope, so you really just need a clear shot of Polaris. So as to get a decent view of M20 & M8 I once set it up under a tree with another tree to the north only having a view of Polaris between branches and it did the job, something I would never have been able to contemplate using Synscan's 3-star polar alignment routine.
I haven't observed the images it takes carefully (I usually wander off with my binoculars to look at something), but it's probably just imaging the same tiny bit of sky around the pole from three different angles and doing some comparative check on how the stars' positions have moved relative to how they should have moved if the mount was aligned properly - it is after all just moving the mount around the RA axis with the DEC axis set to 90° so it can't really be imaging that much of the sky in a field of view of only a few degrees at most.