I would like to suggest other names, to give it more an intuitive 'polar feeling'. But that is up to you.
.OriginX i would name .PoleX / .PoleY. "Pole" is mostly used to point to that point. (i think)
.DeltaX i would name .Radius
.DeltaY i would name .Azimuth. "Angle" is taken. And Azimuth means the angle to a reference angle.
Well the Origin X and Y designate the position of the origin of the polar coordinates (aka the point (0,0)), so I think it's better named that way.
I could name DeltaX and DeltaY, Radius and Angle for clarity purposes. Also the "Angle" is not necessarily taken as it will be Object.PolarCoordinates.Angle
You could add that 'reference angle' (the polar axis, up to you), but i guess that will complicate things for most users. Everyone is used to zero angle as reference.
Say you have two objects under an angle(x1,y1,x2,y2)
Say we can set an expression .ReferenceAngle to that angle. (or leave it to a default zero)
Then we can set .Azimuth with .ReferenceAngle as the angle from where .Azimuth starts to rotate from.
I understand what you mean but I don't think that's really useful. The purpose of the plugin is to allow the use of polar coordinates, not make the act of polar rotation easier. However, you can make that pretty easily, as you can see in the two example capx.
And you can set the "Start" angle from the editor in the behavior's parameters, so it's kinda similar to what you want.