Try what cmshoot said but that's just a manual fix for a deeper problem. It should engage and not move until you move it. It sounds like it needs a little matal message off the safety. Unless it really is the grip. If not try this.
If you take apart the gun partially ( grips and slide the back strap down almost all the way down ) and leave the spring on with the back strap slid almost all the way down but not off the spring, you can see where it will hang up with a flashlight. If you start working on the safety only remove very small amounts of metal at a time. Then try again and remove metal until it works. Remember you can always buy new safety and they're not that expensive so don't be scared to give it a go. I would suggest buying a Wilson Combat replacement ambi safety and see if that works. However, nine times out of 10 when you buy 1911 parts they're not 100% drop in especially the safeties. You could get lucky and it might drop right in. If cmshoot is correct and the grip is causing the problem then that is a simple fix.
If you want to put a nice flared mag well on there you can look at Techwell ( at first it looks like a clothing site but dig into the grips and mag well section ) and they have VZ grips with little divots in them that hold a nice flared mag well in place. It's a $200 edition but it's sweet. I have them on this 1911 that I totally redid the inside with Wilson Combat bulletproof parts in stainless. You can purchase less pronounced mag wells but I like the big one. If I still lived there I'd fix it for you for nothing.
