To help the multi-cam help you, I would first make sure the audio on each clip is loud. You can do this by right clicking on each clip and increase the volume of each so that they're at least in the -12 range. you can also select a bunch of them and do them all at the same time if you want. When trying to sync the clips with the audio, PP has an easier time figuring out where the clips go with better audio.
The second thing I would do is to make sure that when you're creating the multi-cam, make sure you select that one camera that was on the whole time first, then select the others, then right-click and choose create multi-cam. PP uses the audio of that cam to help it sync up the others and also uses that for your main audio of the sequence.
Also, before I do the MC, I usually make all the audio that I'm using for syncing purposes mono. I'm not sure if this helps or hurts PP but I haven't had any issues. You can do this by right-clicking on a clip, choosing Modify, and then Audio Channels. Then you can choose the Mono preset and you should be good.
Also, I do this a lot and thought I would show you my usual settings In the MC dialogue box. I also use the audio sync, which I love.
One more tip: I would try and break up the play in parts as far as the syncing goes. Meaning that if you have say the intro and 1st Act, I would select your main clip, and then only the clips that you have that have that intro and first act. Call that sequence Act 1 (or whatever you want). For the second Act, on your main clip, create an in-point where the 2nd act starts, also only select the clips that go with act 2 and create a second sequence with that. There's much less room for error there and when all the Acts are done you can put them all together on a separate sequence one after another.
Hope this helps.