you deserve a good bike fit
Knowing what I paid for my Santa Cruz I would be so sad if it didn't fit right. Your shop should provide you with a proper fit. They should have assisted you in making the right choice on size. Although it sounds like you did your homework too. You could try moving your seat foward for starters. I am not sure I would rush out and buy a new stem yet. Start with the small adjustments. For example can you tilt the bars back toward you a bit, move the seat. I wonder about the length of the bars in regards to the difficulty with the front wheel coming off the ground. I typically cut an inch of the sides of the handlbars as they are often too wide (and I am not particularly narrow). Of course I wouldn't go cutting either until you know for sure that this is an option you want to take. I also find keeping my elbows angled down on a short steep climb helps prevent the wheel lift too..
If for some reason your shop won't work with you, find a different shop that does professional fits and ask them to help you.
Good Luck