The last heater I installed had 2" of insulation between the outer cover and the tank.
Judging by the the crease on your outer liner, there is no way your glass lined tank would have been harmed.
If you have exhaust fumes, that's a separate issue.
Is the new tank taller, changing the grade on the chimney?
Terry it could be...it is a Kenmore Power Miser 9 ...plumbers are here now replacing 3 inch flue with 4 inch...I hope that helps..he said it would. I wish some of you guys were closer to NH, I know it would get done right!