There are a couple of reasons why you can’t use the Solid Tools to trim this. The first tow is you have the component double wrapped. A component inside a component. The other is there are holes in the surfaces. The dark “lines” are the borders of those holes and there’s matching ones on the other side.
If you fix those holes and explode the unneeded component container you should be good.
Now that I can see your model I see the molding profile is only 0.370 in. tall but you say you want 0.375 for the thickness. Another option that wouldn’t require the component to be solid is to draw a couple of edges on the flat edge face and then use Ctrl+Push/Pull to push the face through. Then select the geometry and Intersect Faces>With Selected followed by deleting what isn’t needed. Here the upper of the two edges on the flat end is 0,375 down from the top face.
After Intersect Faces, waste selected for deletion.
And waste deleted.
It would still be best to fix the holes in the surfaces to make it solid.
By the way, I know this has been brought up previously. Turn off Length Snapping.
It would also be a good idea to purge unused stuff from your model.
And make sure you are using tags correctly. You have a fair amount of geometry that has been tagged. ALL edges and faces should be untagged.
No. Yours isn’t solid. You could start over. I just fixed it by filling in the missing edges and faces.