Handles with the metal connection could only go onto the stem a specific distance. Plastic handles can slide "over" the stem and go on too far without the metal washer. If the handle is contacting the "stop tube" as it is pulling the stem out, then etiher the tube is not on all the way or the handle is going on too far which is what the little washer is supposed to prevent, and the same thing will happen with an extension kit. (you could also cut off the "far end" of the stop tube to make it shorter, but that should not be necessary once you get everything together properly) If the handle is hitting the "trim plate" then either a couple of the washers or an extension kit will cure it.
Thanks for the details of the handle operation. You never realize the intricacies of how seemingly simple things are designed, until you run into a problem and look at it closely. As I said in my post from last night, it appears that the only problem I really had was that the handle I was trying to use was a (plastic sytle) "sink" handle ... not the (plastic style) "tub and shower" handled that I needed.