I discovered that I was outsmarting myself with the green laser pointer that is built into the ASA DDM60 mount's RA axis. I thought it was directly aligned with the axis and was trying to estimate the distance away from the pole that Polaris was, and pointing the laser beam into that empty space where the celestial pole should be. Then, last night, I discovered that the laser actually describes a circle in the sky when you rotate the RA axis. Thinking that the laser was out of alignment, I was contemplating taking the cover plate off and attempting to "realign" the laser with the RA axis.
Before doing that, I searched for some advice on the issue, and finally came up with this statement from ASA in their FAQ forum: "If you turn your RA-axis, the laser will describe a circle on the sky. If you try to place the polar star on that place where Polaris should be actually in relation to the pole you have finalized a raw polar alignment."
So all this time I have been pointing off Polaris where I thought the pole should be, when in reality I should have been pointing directly at Polaris, with the RA mount oriented in such a way to put the center of the circle on the pole. Now I just have to figure out how to position the RA axis to get Polaris tangent to the circle at the right place.
Maybe if I imagine a line from Polaris to Kochab in Draco, and place the counterweight coincident with that line, that will orient the RA axis properly, at least to one side of the circle or the other. I should be able to tell which side is correct by just turning the RA axis and watching the laser describe its circle.
My only other thought is that I should slew the telescope to Polaris, and then move the mount (the tripod for azimuth or the altitude adjustment on the pier) to center the laser on Polaris.
My confusion arose due to the fact that the manual for the mount states that the laser is aligned with the RA axis, and they actually recommend pointing the laser at the empty point in space 0.73 degrees away from Polaris. Yow! Which one do I believe? Obviously, my laser in the DDM60 mount is describing a circle in the sky, so I guess the FAQ answer trumps the manual.