How to beat this roman numeral puzzle?

I have been stuck on this puzzle for far too long and at this point I just want to get past it so I can continue on in this game. The idea is that each roman numeral tile needs to be under its corresponding lock and all tiles must be facing in an up position so that the point is pointing to the lock. I have been able to get the I and IV in place multiple times but I always find myself in a situation where the III and II are flipped and with the way it works, I can't figure out how to get them in their respective positions.

I realize there are probably several guides out there that explain each puzzle step by step, however I do not want to accidentally spoil any of the game, thus would rather not have to comb through a guide to find this one puzzle.

There are essentially two bits to this puzzle: rotate the 2, 3, and 4 tiles 180°, then get them in the proper order.

Rotating the tiles are fairly easy. Each time you move a tile from the right to top, it gets rotated by 90° counter-clockwise, so each tile has to be moved from the right to the top twice.

Getting them in the proper order isn't as straight forward. You can swap positions 1 and 2, and 3 and 4, but not 2 and 3 without also rotating the tile. This means when you perform the second set of rotations, you basically need to insert them in the proper order.

The exact steps are as follows:

1. Rotate 4
2. Rotate 3
3. Rotate 2
4. Move 1 to the final position
5. Rotate 4 and move to final position
6. Rotate 2 and move to final position
7. Finally, rotate 3