I've had a bit of trouble with color on my first piece. It was pretty close, but had too much ash tones in certain light (namely, anything close to natural sunlight).

So, I went to one stylist who added gold. That really didn't do any good, and she did it while the piece was on so some of the gold got onto my bio hair.

I went to another stylist who noticed there was too much gold AND some of the ash/green tones were still showing. They tried adding what I believe was brown.

Now the piece is too dark, and so's the top half of my bio hair.

I got a new piece in that should be better color wise, hopefully. But it has to be better than this.

My question is, is it possible for a stylist to strip all this color from my natural hair to restore the natural color?

There are professional and off the shelf colour restorers that reduce the dye in your hair.
They work on natural hair & replacement hair.
The one I've used is Goldwell Color Remover.
Its a professional product but you can get it on ebay.

But if you're having it done at a salon, they'll have their own brand that they use.

You should be fine.

I have no idea if it was permanent or not. In both cases they just brushed something on my hair, left it for 10-15 minutes, and rinsed it off.

I'm pretty new to color as the most I ever did with my natural hair was highlights.

Do you know if it was something the mixed together using 2 parts or was it something pre mixed?
Its possible it was a colour conditioner corrector.

But if you're going back to a salon to have it sorted, then you really need their advice & assurances it can be done.
They'll know what they used and how to correct it.

Not going to the same salon for the cut-in on the new piece. They are fine for maintenance, but I don't just trust them yet for cut-ins. Going to one of the more well known stylists on this board.