Sorry I didn't really explain myself.
By showing your intentions of making a frame as shown here
It will not keep the original geometry of the frame it will make it worse (relative term) or more relaxed than it was, the center stand is taking the weight off the rear shock so its not sitting correctly and thus unnaturally elevating the headstock. To replicate the original height of the headstock and geometry you need to let it rest on both its original wheels with the original forks in place. You can then measure the height of the headstock from the ground and the trail if need be. To replicate this on a new frame.
I dont think I'm taking a leap in the dark here but the original geometry of this frame could do with sharpening up to get quicker steering more suitable for a cafe racer than a cruiser.
By lowering the headstock, in your case allowing it to sit naturally on the gsxr forks steerer stem , this will achieve the desired improvement is sharpening up the steering.
I dont think you need any frame modifications in that area.
I'm sure someone will come along thats actually fitted different forks to an XV without major frame modification to offer their advise.