One thing you have to watch is,
I do the same thing, or did atleast, with a Glock, it has a longer trigger pull, or atleast a annoying trigger safety, that Para probably has what a 7-8 lb trigger?
You'll find that the first shots, you know, you'll squeeze, but as you go through more and more you'll jerk, and as you do, your shots will start grouping to the left, or atleast going left, since you're apparently right handed, did the same thing with me, just focus on the trigger pull, and consider getting that trigger looked at.
Might be nothing, might be everything.
and I might be wrong, but still, try that out, see if it works, watch your trigger pull and be careful not to jerk with your Index.
EDIT: BTW, the reason I'm really pointing this out, is this is your as you said, first hand gun you've bought or possessed, so, I'm just trying to give you a pointer.
EDIT for the 2nd time (this is getting to be problematic.): A 18Z I known and talked to one day, after I had fired my first hand gun, I said I had a really good grouping, and I was shocked I could shoot well.
His answer surprised me, he said "I'm not at all. " he then proceeded to tell me how beginner Hand Gunners, or people brand new with a firearm, tend to not have formed the bad habits that regular or experienced shooters form and have to break, the trick is, keeping and learning good habits for shooting.
Anyway, Congrats, I'll shut up now, seeing as I don't own a 1911 myself yet.
EDIT For the third time: Sorry, it just hit me I never explained the long trigger pull jerk thing, as you get fatigued, etc, you lose your discipline, or atleast, you do what's comfortable, and as you pull, you'll probably find your grip changes, atleast in the top portion of your hand, and it can move it just that little bit which seems to be the problem, so in closing (yes really, that was it) let me ask you, Were your shots center mast when you started or were they farther out?