Update:
I ended up using the Transform approach I originally found here:
It did work fairly painlessly, despite having many objects and keyframes (almost 2000) in sequencer. However, this method requires duplication, either of the whole sequence, or of all the frames inside the sequence. That’s not ideal for multiple reasons, but it’s the only thing I could figure out. I chose to duplicate the entire sequence, so basically, I have a “forward level sequence” and a “reverse level sequence”.
For anyone who is also trying to do this, here was my approach:
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Find the midpoint of your animation (ex. if your last key is on frame 1200, your midpoint will be frame 600), and put the play marker on your midpoint frame. The “flip” will happen around this point, which is why you want it in the middle if you’re looking for a “mirror” of your animation.
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Select all the keys (the actual keys, not the object layers) you want to “flip.”
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Open the Actions Sequencer menu and choose Transform Selection.
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Type -1 in the far right field, and then click the multiplication (*) button. Your keys should immediately be flipped around the midpoint.
That said, it would still be nice to have a “right-click on a subsequence and choose “reverse”” option, or just make the “-1 play rate” trick work like it apparently used to.