It is amazing how repeating games is actually beneficial...
I have done this game probably 5 times before, but when I did it today, I had a spark that led me to frame this in terms of p going at 6 and then p going at 12.
This is context of realizing that the [R10->~F10] rule, which really means that 10 is either all folk or all rock, can be used to create two options for p at 6, and then 2 options for p at 12.
I decide to have 2 columns, one representing what happens when we have an all folk at 10, and one with an all rock at 10.
I know that I need to show P at 6 and then at 12.
My first set up was with P at 12.
I decide to set up the rock at 10 because I felt that this would be the simplest since only Q and T are left.
I place Q and T at 10, with Q being N stage and T being S stage. I no longer have to worry about the Q immediately following a folk, as no matter how I complete this diagram...that rule will take care of itself because I only have folk left to distribute. I know that G has to come before H, thus the G will go at 6. I now have H and L left, and their order can flip like Q and T, as long as we flip them at the same time.
Now for the folk at 10 with P at 12...
Well I know that I need a vertical block consisting of 2 of 3 folk: GHL.
I know that G cannot be in this block with P at 12. This is because we will have nowhere to place H.
I now know that this block will be of H and L.
I arbitrarily place H in the north with L in the south, knowing that I will probably be able to run the same concept of flipping them. Although I am ready to run another hypothetical if things are too complicated.
I now turn my attention to where Q must go. I know that it must go at the 8 slot, although I do not know which one, n or s.
This is because Q must come immediately after a folk, so its only option is the 8.
I now know that G must be in the 6, as it is the only folk left for Q to follow. This leaves me with T, and I know it must be opposite of L, so T will be n and Q will be s. I now show the flipping aspect, but they must both be flipped when flipping.
Now we need to do the f10 and r10 idea with P going at 6.
I decide to once again do the r10 first because I only have 2 r's left, Q and T.
I arbitrarily put Q in the n and T in the s.
The Q immediately following a folk group rule will be taken care of necessarily with my placement, so we do not have to worry about this one.
I do know that G has to come before H, this means that H must go 12.
We know that G will be in the 8 slot since P is 6. Now we need to accommodate the T-L different stage rule, so I place L in the n and G in the s. I add the flipping aspect to it.
Now we do the last one, P at 6 with the f10 grouping.
I realize that G cannot go with H in this vertical block of folk at 10, so what about L with G? This would force H into the 12 spot. But then we will not be able to have Q immediately follow a folk! So G cannot be in this f10 block once again. So it will be L and H. I arbitrarily place H in the n and L in the s.
I can arrive at my next deduction in either thought process:
1) The Q has to immediately follow a folk. This is only possible with Q going at 12. This forces T and G into the 8 slot, which would make us adhere to the T-L rule and use our flipping aspect.
2) We realize that T must be opposite stage of L, which requires T being in north at 8. We also know that G must come before H, which means that G will be south at 8. Only one variable left to place, the Q, and it can validly go at 12 as it follows folk.
So we have four frames that have reversible pieces and encompass every scenario. In hindsight, I would have placed the 8 and 10 slots in a block and had one reversible handle on it to denote its reversibility as one way with both slots going at the same time.