You may already have noticed, seeing the previews or messing with the models themselves, that there are a few more complicated features that are made to workaround SFM's limitations and push it to its limits.
All of these involve animated textures, complex bodygroups, and bodygroup skin lists. I will address them here.

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All models including skins now have a complimentary Skin List included in the Bodygroups tab!
Each of them are numbered with their correct skin. Some models that have INVERSE variants will also have their skins listed there.

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Even though I have added a bunch more skins that are not actually existent in the game, I have also left the ability for simple solid-colored models to have a unique color choice given by you!

If the model has a listed "custom" color skin in the Skin List, this means you can easily edit the color!
The texture will appear white, which is on purpose. It allows you to add a specific Element Viewer material property that darkens the white into whatever color you choose.

1. Right-click your model, and select the Custom skin (usually the last skin) on the skin list. The material that can be customized should now appear white in the viewport.
   
2. Right-click your model in Animation Set Editor. Select "Override Materials". Right-click again, and select "Show in Element Viewer" > "Model".
   
3. Look for the green name of the custom material. This will either be labeled "custom", or "white", for obvious reasons.
   
4. Right-click over the green name of the material, and create a new attribute: a color attribute named "$color".
   
5. Click on the color box to replace the color with any RGB value you desire!

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So, quite a few of the models got really heavy when it came to exporting it. Heavy, as in, it passed the object poly limit tremendously. Or, the skin groups have different UVs, so I had to just put them in completely different bodygroups.

I'm looking at you, fence_big.mdl and fence_small.mdl.

Therefore, I've torn up the models a bit into multiple sections of bodygroups, which should all be enabled or disabled together. I couldn't find a workaround for this, and I don't think there is.
Just enable/disable them there, and you should be good.

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When SFM has multiple objects with a similar animated texture, all objects will always play the same frame. This may not look good and may limit creativity.
I want to animate frames. Do you, too? Good. I found a solution after searching on Google for a while.

Credits to Detonatress here on Steam for finding a solution, and using it on his TV model. I tweaked it just a bit but now you can easily edit the textures just by using Element Viewer.

1. Right-click your model in Animation Set Editor. Select "Override Materials". Right-click again, and select "Show in Element Viewer" > "Model".
   
2. Under the material dropdown, find the texture you wish to edit/animate. You should make 2 new attributes by right clicking the green material:
   ----a. a bool named "$manual", and
   ----b. a float named "$frame".
   
3. Checking (enabling) manual will override the automatically-playing texture, and allow you to edit the frame by changing its number.
   
4. If you wish to edit this as a value in the Graph Editor, right-click the green material again, and select "Create AnimationSet for Element".
   
5. You will be prompted to enter a minimum and maximum framerate, to set slider borders. You can find this number in the material's .vmt, or at the end of this section in the table.
   
6. Ensure "Show Scene Hiearchy" in the Animation Set Editor is disabled. You won't be able to find the newly-created slider unless you do.

Here is the table for framerate values you should enter: