Working Backwards?

Ok, so you find an interesting mating pattern, and want to compose a study or mate in x) around it.

Can somebody give insight on thought processes that lead backwards from the final position to a totally different starting postion maybe a dozen moves before?

I'd be curious to see what members can come up with in this position, I will post the original later: (ignore the White to move bit, please)

A series of exchanges took place on e4, with the last move being the white bishop capturing a blac piece?

Hmm... Well, clearly Black's last move can't have been a pawn move. A series of exchanges would be very heavy to have in a study, if you know what I mean. Also, if the last move was something-b8, the King would have taken, not the Bishop. This means Black's King was just distracted to a8 somehow. It had to have come from b7, but that means the only thing White could have just MOVED to a8 was a Knight, which would be a draw if Black didn't take the Knight. I have to go now, I'll be back later.

Look up NN - Pillsbury blindfold simul 1899. Final moves Qf1+ Bg1 Qf3+ Bxf3 Bxf3#

Ok, a hint:

The last move was Kxa8, not forced, but everything else loses too. This is just the pretiest finale in a pretty combination.

10 moves ago the Black King was on f6, and Black looked like winning at 1st glance. (V Korolkov)

I would say there was a Rook on a8 a while ago, but it was trapped. That is the only reasonable finish I can think of. Now I have to figure out how to get there.

OK, here's sort of a general idea. Clearly, though, it needs more - it starts with an obvious capture and it doesn't have a real idea in it yet. It's just a way of getting to a position with more ways to "step backward". I'll keep looking.

In the Korolkov study the bishop ends on c6, not on e4

You're right, of course Heinzie, the Bishop ends on c6! (From: Tal's winning chess combinations)

The position looks as if it arose in actual play. It seems Black has just sacrificed a Rook and the pawns are moving irresistably  ahead to queen. One also gets the impression Black should win, since the d pawn is easily stopped by the King. But

Now, let me rephrase my original question.

Did the composer start with the final posion, and reverse engineer(?) from there?

Was it perhaps a position in a game that inspired this?

What is the method of finding a starting position that is fraught with danger, traps and snares?

Will I just never become close to doing anything like this? :(

I struggle a lot with this too, and I'd be quite curious to know if anyone has an answer. I think this is just the hard part of composing.

I usually start with a pattern or a tactic that I have seen in a game or found in an analysis. From there, I start to work myself back some moves. Here is an example:
I wanted to make a position that the engine would misevaluate. I knew that engines usually don't understand when a piece is entirely useless, if there is no immediate way to exploit it. One such case is this:

The black bishop is entombed. However, this isn't enough to troll the engine. We need more useless pieces.

For some reason, I was thinking that it was more aestethically pleasing if the pieces were entombed on the kingside.

Now, I need to use this motif to create something. After some thinking and trying, I got this position:

So how do we reach this position? I imagined some hanging the knight on g6 with equal material, like this:

But I soon realized it was impossible; white could play g6 in all settings. So, I needed another way. One way was preventing black from playing ...g5 and activating their pieces, by blocking the g6 pawn. If I in the process could hang a piece, it would be good. So I started wondering what to hang. A knight isn't ideal, since it could easily move away and win the c6 pawn. So, what if I can hang the bishop instead? A light-squared bishop looks artificial, since white already has one. So, it is better if the bishop is hanged on f8 or d8. On f8, it could move to g7 and win the poor h8 knight, so only d8 works. After some thinking about what would take the most time for white to maneuver the forces (in order to make the engine count more), I came up with this position, which is actually very hard for Stockfish to solve!

I didn't lengthen it any further, since this felt more aestethic with a short puzzle.
This was my thought process. I am not sure whether the big composers use the same tecnique.