The Menu: Image > Trim command seems to offer results that are similar, yet still different, from the Menu: File > Automate > Crop and Straighten Photos command.
The Trim command does does not seem to address the occasional need to straighten or make edges parallel and congruent.
Here are examples of Trim and Crop and Straighten Photos:
The Automate > Crop and Straighten tool, as you have found out, has its limitations and requires that sides be parallel in the x, y planes and the corner lines in those plane perpendicular, not a parallelogram.
Quick illustration of Automate C&S. Top dealing with an image that complies with the parallel and perpendicular rules but is just skewed, C&S does a credible job. Bottom images converging verticals confuses but still it manages to find the top and bottom parallel lines.
I believe the problem really lies in your 'rig' not being parallel in x and y axis, or the placement of slides leads to slight keystoning which automate C&S will not cure.
If the slide image contains really noticeable horizontal or vertical planes and those planes are parallel to the sides of the slide mount then why not just crop in camera to eliminate slide edges and eliminate the need to C&S in post?
Otherwise, you may find the Perspective Warp is your friend if it is available in your PS version, but of course, just a manual solution as you have to select corners before pressing the Auto icon