I study palgwe il, palgwe ee, palgwe sam, palgwe sa, palgwe oh, palgwe yuk palgwe jang, palgwe pal chil, and palgwe pal jang. These are just the ones that I closely study. I study others as well.
That's not "lots", some of those are not even Palgwae forms ("palgwe [sic] pal chil", for example), and those are not all mirrored. In fact, most of them are not. Let's look at just the easiest example, shall we?
In Poomsae Palwgae (note spelling) Ee Jang, step 5 is a right Back Stance with a left Low Knifehand Block. This is not mirrored.
Step 6 is a left Back Stance with a double knifehand middle block. This is not mirrored.
Step 13 is a right Back Stance with a left Supported Low Block. This is not mirrored.
Step 14 is a left Back Stance with a right Supported Middle Block. This is not mirrored.
Step 15 is a left Front Stance with a left Outside-Inside Middle Block. This is not mirrored.
There are only 20 steps in the form, of which 25% are not mirrored. That doesn't seem to support your claim at all...
The Palgwae forms are really not mirrored forms, despite what you've claimed. If you like, I can go through each one for you. I'm likely to limit that to one non-mirrored technique per form though, because that's sufficient to disprove your claims without taking much effort on my part.
Just for reference, I hold a 7th Dan from the MooDukKwan. We still teach the original Palgwae forms, and I am the author of two books on the MooDukKwan. My Kwanjangnim was a direct student under GM Hwang Kee, the founder of the MooDukKwan.