The Limited is the best gun for Limited (and $1,100 is a good price for a new one), but if you're determined to get a Production gun and turn it into a Limited gun, I think you'd be happier with the Stock III. Between the Stock II and the Limited, it's not just a 1/4" of sight radius, but also a 1/4" of barrel, slide and dust cover which significantly effects the feel.
Don't forget the Limited has the same indestructible hard chrome finish as the Stock II, while the Stock III is blued which wears off and starts to rust with heavy use.
The performance differences, real or imagined, are going to be minimal between these guns, but the resale value will be much higher on a Limited set up for Limited.
If the initial cash outlay is such a big deal for you, why are you buying new? There are great deals on used setups in the classifieds here. In fact I think there's a Tactical Sports right in there right now I would recommend over any of these Tanfoglio choices in terms of value and performance.