Actually only experiments will help to find the right settings here. On CentiLeo side we will implement a lot of AOVs (extra images), mask images, some funtionality to combine them in the output. It's all possible because we have a very good architecture to support the render and output of really many images at once.

I tried disabling all my lights, and this seems to show this now for the alpha.
But why would the lights on the tree not affect the shadow on the regular plane but burn out all shadow on the shadow catcher plane?
Does it have something to do with that each of the cloned lights on the tree has shadow matte weight?

But even stranger is when I disable the lights I am left with a new shadow that shouldn't exist.
There should only be a shadow behind the tree, but no matter what I do my HDRi is somehow making a shadow in front of the tree that I cannot remove, but it only shows up in the alpha when I enable shadow catcher. Otherwise the shadow isn't there.

And this shadow that shouldn't exist appears even if I turn the HDRi multiplier down to almost zero, including the shadow weight for it.

That remaining shadow in front of the tree is probably casted using the light source that is not switched off. The bottom line status bar says there are 8 light sources in the scene.
How did you implemented the colored light sources on the tree?
1) If they are regular cinema omni lights with centileo light tags then by default they will cast shadows on the shadow catcher. In this case you can set shadow catcher matte weight to zero for all such lights.
2) If you have implemented the colored light sources on the tree with the spheres and emission material then they will not produce the shadows for the shadow catcher object and will not affect it. This is a preffered way for render speed for this scene if you don't enable imprortance sampling for such emission materials because their lighting is local.
If you want the shadow catcher object to receive the shadow only from the one light source or Sky HDRI then only this object (using CentiLeo light tag or environment tag) should have shadow catcher / matte weight equal to 1. And all other unwanted light sources should have shadow catcher / matte weight equal to zero.

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ssjenforcer wrote: Ok, I had disabled the check on my cloner objects but neglected to also uncheck my lights that were childs of the cloner, and so they were still emitting light in the scene and casting that shadow. Turning all their shadow weights to 0 fixes everything.

Basically in the case for this scene it can be faster to make these colored light souces on the Christmass tree with sphere objects and apply an Emission material on them with "imtportance sample" off. The render may become faster if these lights produce local lighting, not global.

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ssjenforcer wrote: It was just confusing me that the beauty showed a certain shadow and the alpha showed extra shadows. Is there any reason that the two modes would show different shadows, when having and not having shadow catcher enabled? Is there a way to make them show the same shadows in both modes, particularly when viewing IPR?

They should be the same on the shadow catcher plane. But they may look different based on the color conditions, the alpha channel is black and white and it may show the shadow masks more clearly on a black background.

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ssjenforcer wrote: Or is the simplest way to remember to change my shadow weights for every light source?

Basically only few types of light sources can contribute to the shadow strength that is casted to the shadow catcher object:
1) Sky + HDRI using CentiLeo environment tag, it has shadow weight.
2) Directional (Infinite) regular light with CentiLeo light tag, it has has shadow weight.
3) Regular light of Omni type with CentiLeo light tag, it has has shadow weight.
Other types of light sources (area, spot) don't produce shadows on the shadow catcher plane. If you want to exclude some lights from producing the shadows then just make shadow weight equal to zero. Or make it a smaller number to make this shadow weaker compared to others. This feature is nice itself and has potential to future improvement.

In case you use node material editor there is an Emission material node that can be used to plug into Output node or it can be combined with Material using MixMaterial.
Otherwise you can use simple not-node based materials, this way an Emission channel is available inside the Standard CentiLeo Material together with Reflection, Diffuse, Alpha and other channels.

These two screenshots describe two ways of Emission material setup:
1) Using nodes. Here the emission node is connected using the mix material with a bitmap to manage where it's an emission or reflective material. To avoid hiding the bottom left menu of available shaders just click at the button inside red rectangle to stick it on top of other windows. This is native Cinema 4D R25 interface feature, not CentiLeo. To my mind in R23 it was more convenient node interface.


2) This picture shows how to setup emission material using standard old centileo material, here a checkbox on the left is needed to be enabled and manage all the settings in Emission tab. Of course managing complex texture relationships with nodes is much easier.