I know for my eod I had to put a ton of pressure on my visor to make it conform to the helmet, and trying to build up the helmet around the visor to leave it at its original curve would have looked rather silly. Unfortunately with an eva helmet you don't have the luxury of manhandling the visor into place and bolting it down, so modifying the visor or making one from scratch is your only option.
Is all of your visor needed to fit your helmet? If you have any scrap pieces, you could test out adding heat to see if it distorts the tint of the visor or the visibility of it. If you do not, you might just have to give it a go on your intact visor and hope for the best, accepting that there is a chance it may not work. I'd give it a day or two to see if anyone else chimes in first! Most motorcycle lenses are made from polycarbonate, which I believe can be molded by heat. Unfortunately if your heat is uneven and parts of the visor bend at differentrates/angles, that will cause the vision to be distorted. The tint is your other dilemma, and I'm not familiar enough with it to give much insight.