The last ARR story dungeon requires 90 for entry, the last HW story dungeon 230, and the last SB dungeon will probably be 360 if it maintains the current pattern.

Therefore HW leveling dungeons should require absolutely no less than 90, SB absolutely no less than 230, and ShB absolutely no less than 360. But really, if we assume these minimums are met, the real problem point is going to be the third dungeon of each set, where things start to hit pretty hard even if you are at the former expansion's max (e.g., running 130 gear in Aery or 270 gear in Bardam's Mettle).

So I would go with something like this:

Let prevStory = the iLv requirement to enter the final story dungeon of the previous expansion
let prevMax = the maximum iLv achievable in the previous expansion

First leveling dungeon: prevStory + 10
Second leveling dungeon: prevStory + 10
Third leveling dungeon: prevMax
Fourth Leveling dungeon: prevMax
Fifth leveling dungeon: prevMax + 10

With how much gear the story quests throw at you, and the autogear at the end of the leveling dungeons, these shouldn't pose a significant burden on anyone who's playing even casually.