If my games get into that period, I like to use bombers instead of artillery. That way you can move your mech inf and tanks fast, not having to wait for artillery to catch up. The town you're attacking will be at 0% defenses, and all the defenders at half strength by the time your armour/mech inf roll up to the gates. Now I understand why in real war air supremacy is crucial.
The best part is that even if your bomber gets intercepted, usually it won't be shot down, only reduced by half or more HP. Just let it rest, and continue the bombing campaign with other bombers.