Let me help guide your way of thinking a little bit. A 1G GT head is a 1.9 HO head. However, its still a SOHC head. As you know your 2G GT has a DOHC head. Here´s the difference. A DOHC head is more volumetrically efficient, ie it has a higher VE.
A SOHC head is generally 45-75% efficient. Usually HO heads flow at the top or slightly above the VE of that head´s normal characteristics. But, a DOHC is generally 70-95% efficient! So by keeping a DOHC head you´re going to be more efficient. So by boring over your motor to add displacement, if you were to drop the SOHC head, you would LOSING power, in theory.
Another thing I´ve learned too. Stroking isn´t all that. In fact, getting the 1.8 to a 1.9 is a waste of your time as far as building a bottom end. Stroking is where its at for our motors. I had a friend of mine thats a genious when it comes to building big blocks, he thinks with a TON of work and a whole lotta cash we can go to a 4" stroke with the motor, and possibly go .03 over on the bore. Hopefully hitting a 2.5 -3.0L displacement. Here´s another thing I found by pencil pushing the theory.
If you could increase the VE of the head by 10% and hit like a 95-97% VE efficiency and increase the rev range another 1k revs, you can actually create more HP on a peak then by stroking the bottom end. That´s not the whole picture though, by building the bottom end you can build a motor that will support the higher revs, take more boost, and provide more Torque, and torque is the key to making a vulgar display of power.