You can't do what you want by making a sync clip with a multicam clip and another clip.
There are a few of different ways to do this. Basically the easiest way to do this using two copies of the multicam clip.
The first thing you want to do is go to Playback preferences and uncheck background rendering, and uncheck create optimized media for multicam clips. Always leave these off.
You will have a lot of tracks playing simultaneously, so you will probably want to create proxy media for your shots and work using proxy files. Select the shots you're going to work with, right-click and choose Transcode Media. Select proxy files. Switch the Viewer to Proxy Preferred in the View menu in the upper right. Once that's done you're ready to being.
Start by making the multicam clip, combining your clips together with the PIP clip inside the multicam to sync them up.
Open the multicam clip, select the PIP shot and scale and position it how you would like.
Put the multicam in the project and edit the primary storyline using the Angle Viewer to select the shots you want, leaving aside the PIP shot. Don't switch to it.
When you have a rough cut finished, Option drag one of the shots upward, maybe the first one, so you have a copy of the multicam as a connected clip.
Right-click on the connected multicam clip and select Active Video Angle to choose the PIP shot.
Stretch it out the length of the edit. You now have the PIP on top of the edit throughout the length of the project.
If you don't want it throughout the length of the project, use the blade tool to cut and delete what you don't need.
That should work assuming I understood the problem correctly.
