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Once you remove the slide pins the calipers should just slide off so I'm not sure what's causing yours not to move.
At a pinch you could remove the caliper bracket retaining bolts (15 mm IIRC) and take the whole assembly off, then see if you can pry the calipers off the brackets.
Apparently some have done this as their preferred method of changing the front brake pads, I tried it once on my old XFR but for the life of me I could not get the old brake pads out, the caliper bracket got in the way too much.
Conversely I have changed the pads and/or discs on the front 380 mm brakes on the old XFR and the current F-Type several times just by doing what you have done so far, and never had a problem with the calipers being stuck.
I suspect you are going to have to get the hammer out and give the calipers a small whack or two, I suggest you try a rubber mallet first!