Interesting... A couple of weeks ago I bought the Orion U-Mount, which looks very similar:
I could not decide between that and the APM mount:
They both look similar and reviews seem to indicate that there not very different. I decided to get the Orion because it was on sale for $429, vs. $650 for the APM mount, quite a difference.
Previously, I was using this APM mount for my APM 70mm binoculars:
(there is a similar version for the 100mm APM binoculars)
What I noticed with both mounts is what you are describing: The rotation around the vertical axis (azimuth) is smooth in both mounts, but the rotation around the horizontal axis (altitude) is not smooth. This is true in both mounts. I was wondering if the APM mount is better. Maybe it is the way the mounts are designed. Like you say, I have both locks fully unlocked and I still cannot get a smooth movement. It is not as bad as you describe, but not as smooth as I would have liked it to be. It is OK at lower magnifications but if you are working at higher magnifications, it can be a problem.
Regarding lifting it up the mount to move, yes, I have the same issue with the Orion mounts. I have to be careful not to pop the thing out of its base. My 70mm APM binoculars are not as heavy as your 100mm so moving the whole thing is not a big issue. But to be safe, I would remove the binoculars first before moving the tripod. Removing the binoculars is not too complicated or time consuming with these mounts.
The bottom line is that the mount that you bought sounds typical and looks like the Orion and APM U-mount. Similar issues.
I wonder if someone can tell us if the more expensive APM mount is better than the Orion U-mount or your TS-Optic mount.