I used to own a 4001 many years ago and although it was a really bad example I persevered. I put up with the thick neck and the fact that I could never get the intonation right on the E string because of the 'sound'. I tried fitting heavier strings and while setting the relief one of the truss rods broke. Got a new truss rod and installed it only for the finger board to start lifting off as I adjusted the new truss rod. If I put super light strings on, it was OK, if not, it was unplayable. It was stolen in that condition and I hope the thief was happy with his new unplayable, left handed, fireglow, 4001.
From my experience, I'd be wary of putting on heavier gauge strings. I believe also, that the 4003 is a 4001 with a more manly neck for this very reason.