I'm certainly no bike fit expert, but you absolutely want a correct fit. Do you have any hand numbness after a long time in the saddle? That'd be another sign of being too far forward.
Sounds like you have two options. The obvious one would be a new stem; I haven't ever done that so I can't really opine BUT try to get one that doesn't require all your controls to come off the bars to swap out. The other option is a seatpost with less (or no) "setback". That I have played with on my "winter" bike and it's easy and cheap if you just try inexpensive steel seatposts at least until you find what works. Many seatposts have a ton of setback so depending on what you have going on now, this could be your huckleberry.
The other thing you are changing there, though, is the geometric relationship between basically your pelvis and the center of rotation of the cranks.... so just watch your knees at first for signs of strain.
You could always pay a pro to fit you. I found those guys a bit woo-woo for my tastes but that's probably just the couple guys I talked to. Certainly, it can be approached as a science and there are some very astute bike fitters out there.
