Hello, I was running into the same problem as you and used Adam’s solution as well. However, I was wondering if you had found a way to better streamline this process? I’ve attached a screenshot to illustrate my problem:

For the connect function to work properly, it seems I need to select the rounding + caps of each object group. That is, if I shift select all the paths and connect, it will not work right. I have to manually twirl down each path/rounding, so that I am able to select all the caps+rounding+paths for it to properly connect.
This is a process that I’ve had to repeat countless times whenever creating a set of 3D typography. Was just wondering if you had found a faster or easier way to do this, thanks!