Thanks Gerry and Joachim for answering this question so I don't spin my wheels testing things. It's frustrating that this capability (for an object to access Properties of an instance) is only available in Labels and Zones.
The specific application in which this came up was the question of how to represent a Dutch Door, in which the upper part of the door panel can rotate open while the lower part remains closed.
The approach I took was to convert a standard ornamental door leaf into a morph (actually I converted the entire door, then removed the frame) and split it into two parts (upper and lower). I was able to save these parts into two new custom door panel objects, and edit the scripts to remove the automatic resize/stretch. This allowed me to place either panel as a door leaf, without having them resize to fit the opening.
I then inserted lines into the lower custom door panel script to call the upper one (placing it at the right elevation) and rotate it to an arbitrary angle.
I wanted to give the user an option to input the angle in the actual door instance, so I added a new angle parameter into a copy of the original door object. However, I found that the standard Graphisoft door scripting calls a series of macros (about 3 or 4 intermediate ones) before actually calling the door leaf object. To pass along the new angle parameter, I created copies of each of these macros and added the new parameter to each, and edited the CALL parameter to use the new copy of the child macro. It took a while to work out, but it eventually worked.
However, as a practical matter, this is way too much effort. If I could simply add a Property to doors that allowed a user to input a rotation angle, and pull that property in the door leaf script, it would mean that just a few lines of code in the door leaf object would do the trick.
Anyway, it's all a bit frustrating at the moment, however I appreciate the information that each of you shared.