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You describe a couple of things. First, the tendency to "pull my body up." If you mean you're not staying down in your stance, you may have lack of flexibility in the lower back. If that's the case, exercises can help.
You have a 12 HDCP, so you have the basics of the game down. Given this, and your above-aveage height, you might consider a full fitting for clubs. That way, you can find your lie angle and shaft length recipe for irons, plus proper grip thickness.
Once you have the fitter's recommendations, you can decide if it's cheaper to lengthen the irons or simply get fit for a new set. Some irons models can be bent, others can't. Those which can't be bent tend to have brittle metal in the head, or an unusual hosel design which would cause the bending tool to damage the club.
Bending would probably be covered by a loft and lie check, and shaft length increased by putting extenders in the butt. The people at GolfWorks, however, caution against extending shafts by more than one inch because of safety concerns.
Note than lengthening the shaft will increase swingweight about three points for every half-inch added.
Loft and lie could run $5 to $8 a club / and shaft lengthening could run $10 a club, unless you could get a volume discount; if you got a combo shaft lengthening plus regrip, you might save a couple of $$ a club. Regrip labor would be maybe $3, plus cost of a new grip at least $5 / swingweight change $8(??).
In the end... $8 + $10 + $8 + $8 = $34 a club if all changes are needed. So, you might be better to trade in your current irons and get a new set that fits your body and swing.
You might need 2 inches on the clubs...
And the clubs will feel a lot heavier, which if you are playing well at the moment wont be a good thing. I would have thought a reshafting with either dynamic gold super light or probably graphite shafts would be called for as a minimum
Research your area and find best fitter around who will spend time with you. Money spent on a great fitting will pay dividends for years.
Like someone said earlier...get fitted for many reasons but simply lenghtening your clubs will cause the following and you need to be aware of this:
1) For every 1/2 inch it will increase your irons 2-3 swing weights
2) For every 1/2 inch it makes your clubs 1 degree upright
So you need to be careful with just adding length as an alternative...just my 2 cents as I am 6'4. My fit is somewhere around 1/4 to 1/2 inch long as compared to standard (what is that any more???) and I am around 1-2 degrees upright...the reason I wrote "around" is becuase it depends on the manufacturer and how they measure things. So for instance I have bought a standard set off the floor before and had them add 1/2 inch whoch gave me 1 deg upright and I like my swing weights a little heavier so that worked for me.