Cut overlapping ranges and paste (cut) values only

Hello everyone

Let's say that I have a range full of entries or blanks (numbers, strings, dates, etc.) in "A1:A10".
Now, given some conditions, I have to 'move' that range one row down (or more), such that the data ends up in "A2:A11".

To not mess up my conditional formatting, ONLY the values should be cut/ moved!

I tried

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Problem?
It does move the values, which is nice, but it leaves the ones above untouched. I could fix this with smart indexing, but my code is already pretty complex, so I'd like to avoid any more indexes if possible.

I'd wish for something like this

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to only cut/ paste values, such as:

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But, the last code does not work with 'Cut', only with 'Copy' ... this is freaking me out

Help is much appreciated?
Thank you

Since you are only moving one cell down...

How about...

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...where you are simple copying, pasting the values, and then clearing A1