Key question: Why are you moving the receptacle?
If you are moving it because the old location will be permanently covered, e.g., by a kitchen cabinet, then you have to deal with the various ways of making it work without using the old junction box.
On the other hand, if you really are adding a new receptacle and there is nothing wrong with the old location, except ease of use, then use the old junction box to add a new cable. The old junction box will need to remain accessible. It can be blocked by movable furniture but not by permanent cabinets or covered in drywall, etc.
In fact, nobody ever complained about too many receptacles. So unless there is a real safety reason (hard to imagine, but you never know...), you can leave the receptacle in place and chain (pigtail or 2nd set of screws) a short cable from the existing junction box to the new receptacle/junction box.
I had a recent similar situation. I wanted to add a receptacle for phone chargers in a bedrroom, and the existing receptacle was barely in the right place on the wall horizontally but by moving it up a foot or so (non-standard, but who cares) it avoided any issue of bed location. I actually replaced the existing receptacle - it was old, wired incorrectly (hot/neutral reverse), grounded incorrectly (ground was functional but used a white wire to the box instead of green or bare), definitely a previous DIY set of mistakes (as I have found frequently in my house). Then I added a short 12/2 to the new receptacle higher up on the wall in a new metal box.