It might. Why did you move the saddle back if the reach is too much for you? Are you sure this was the right thing to do?

We can't really advise you on fit on the internet, especially without seeing pictures of you on the bike. You need to have someone look at you who knows what they're looking at. But yes, flipping the stem, or getting a shorter one, might work.

Unlikely that you should think about getting the smaller bike, though. The shorter headtube would mean that you'd have a bigger drop from saddle to handlebars, and that would give you a less upright posture and increase the pressure on your back and hands.