Earlier quoted context omitted.
We similarly ditched Risk, or actually, its Italian variant RisiKo ( https://en.wikipedia.org/wiki/RisiKo !). This variant gives differentiated goals for each player (e.g., "conquer 3 continents", or "defeat the Blue army"), which in principle should make the game shorter. But it also allows the defender to throw 3 dice (if they have at least 3 armies), making battles much harder for the attacker. In our group we the…
Up to 3 dice for defence is the standard rule. I think the standard game has several different types of victory, but the one you describe is in there in the British version.
The standard rule is up to 3 for attack, up to 2 for defence.