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Will the 6.5mm difference in reach be affected by the different top tube lengths - 560, 582?
No, the top tube length difference will affect how you set up the saddle relative to the seat tube. You may need a post with more set back on the new bike to keep the saddle in the same place relative to the BB, due to the slightly steeper seat tube angle.
will the stack height play a part in this?
The huge difference in stack needs to be accounted for if you're planning to use exactly the same position. Typically, you'd get most of that dialled out by changing to a different stem angle. You can mess with that stuff here for yourself as we don't know what your current angle is, but for example if you have 100mm×-17° on the tarmac, then 100mm×+6° is going to be pretty close to leaving the bars where they are and accommodating the 6.5mm less reach and 40.5mm less stack of the new frame. Bear in mind that stem manufacturers can't hold better than ±2mm on forged stem lengths, and none of them agrees on where the length and angle are measured from, so don't get hung up on the last mm. Your body changes more than that from morning to evening anyway.
There's only 6.5mm difference in reach, so that's not going to cause any real trouble. 100mm stem on a 58 is verging on short, 110mm on a 56 is right on the #tester_approved 5:1 ratio of frame size to stem length.