I have a few suggestions for you, but first of all understand that solids don't have an intrinsic position and rotation per se. Their position and rotation is really whatever you want them to be.
However, take a look at AcDb3dSolid::getMassProp...you'll probably need to research what some of these return values mean, but perhaps you can derive something like rotation relative to the x y and z axes using one or more of them. And of course 'centroid' should give you a useable position. You'll also need to derive some kind of normal vector for rotation to mean anything.
My second suggestion is to simply put the solid into a block right after you create it, or make a "helper" block that's transformed whenever you transform the solid, and then the block itself can give you a position, normal, and rotation.