I’m currently trying to get the last stone (which I assume is 0.) However, if you ever try playing 0 to grab it, you end up ending the level and not being able to copy it.

apparently there is also an unintended solution, that I discovered by accident

I used three 1s, a 27, a 73, three 59s, tweezers, and X.

First, reset until you have 59 and something else as a starting hand, play 59, and end turn. Then, if you have 27 in your hand, play it, cycling out any 1s. The same turn, play 73 (which suppresses the next card played and brings your energy to 0) and X, which becomes a suppressed 0 safe for extraction.

I was having trouble with this, but I managed to figure it out.

For anyone struggling, read the latter part of the description for the tongs you get from the lab.  It's easy to ignore because it normally doesn't do anything.  It's only in the case of these last two stones that it matters.