You're not alone. I lost my progress on both Quell and Quell Reflect right after an update that added the jewels. Every single level has got a silver medal now, so I can still access all of them. I also still have the achievements I had before. But what I lost were the gold medals, the replays and the coins.

It is definitely possible in 27 moves. It is a better solution found after the game was released. The makers of Quell updated the perfect amount of moves a while after that discovery. The solution video is before that update. You can check the top comments on how to complete it in 27 moves. It is more fun discovering it for yourself of course :)

In 33 moves. (perfect 34)

Testament Stage 2 level 1 "Visiting Time"

SOLUTION:
Drop 1 is on the left, drop 2 on the right.

1: R
1: U
2: R
2: U
2: R
2: U
2: L
1: D
1: L
1: D
2: D
2: R

Now here's the tricky part. You need to block the gender block from going completely to the other side. Timing is key.

1: R and then immediately 2: U
2: L
2: D
2: R
2: D
2: L
1: D
1: L
1: U
1: L
1: U
1: R
1: D
1: R
1: D
1: R
1: U
1: L
1: U
1: R

There ya go :)

I found a way to do Visiting Time in 33 moves using this technique. I put my solution on the "Which Quell Memento levels have been solved 'better than perfect'?" topic.

In 20 moves. (perfect 22)

A Cold Heart Stage 3 level 1 "separate ways"

SOLUTION:
Drop 1 is all the way on the left, drop 2 in the middle.

1: L
1: U
1: R
1: D
1: R
1: D
2: L
2: U
2: L

Now here is the tricky part. You need to block #2 to it's death with #1. You need to time this exactly right.

2: D and a millisecond after that 1: L
1: U
1: R
1: U
2: R
2: D
2: L
2: D
2: R
2: U

There ya go :)