tube size doesn't make a difference as the rings are measured from the center of the scope tube to where it touches the base. I had a longer bolt handle threaded on to my rifle as I had the same issue, but as you're staying with a Crossfire the eyepiece thickness should be the same. It's only the objective end that will be a larger diameter. Going from 40mm to 56mm you only need 8mm more clearance. If I were in your position I would measure the gap between the current 40mm scope and your barrel. Then figure out the height of your current rings and then compare that to the specs for whatever model of rings you're going with. Vortex has their ring heights on their website in both inches and mm.
So say you were using Vortex hunter medium rings that have a height of 24mm and you measured and you have a gap of 4mm between your current scope and the barrel. If you went to their high rings (31mm in height) you would end up with your new scope being 1mm closer to touching your barrel all said and done. I hope that makes sense, that's how I typically work out what height rings I need when buying a new scope and the only time it's let me down is when the new scope was significantly shorter than the old one, resulting in the bell of the new scope not clearing the rail.
