I don't think removing the tantrum spiral entirely is a good idea. It should be a serious threat no matter what type of map you're on.
The basic idea is that there's a threshold level of unhappiness. When you reach this threshold, the dwarf in question is ready to get the fuck out of dodge, and will do so at the next available caravan. Some things can tie them down (given dwarven morals). If a dwarf is married or has children who are happy and not ready to leave, the dwarf will stay. If the dwarf is in a position of authority, the sheriff, the mayor, etc, they'll not leave. (breaking oaths and treason are punishable by death to dwarves, it's a serious no-no, so a dwarf in a position of authority will stick there even if he's miserable). As long as the above two conditions aren't met, a dwarf will leave with the next caravan. It should be noted that dwarves will only NOT leave if they have a happy SPOUSE. They'll leave if they have happy adult children (who will stay) or happy parents (who will stay) or babies/nonadult children (who will leave with the pair of unhappy parents, or the single parent).
Now, if they aren't made happy soon enough, they'll eventually reach the next level of unhappiness, which is tantruming. If they continue to spiral down into unhappiness, they'll eventually go mad.
How does that sound to everyone? That way tantrum spirals -are- possible, but they are far more unlikely, and more realistic as well.
So, to recap.
1) Has the dwarf reached the first level of true unhappiness? (if yes: go to 2, if no: go to 7)
2) Is the dwarf a child (if yes: go to 7, if no: go to 3)
3) Is the dwarf married to a still living, and still happy, spouse? (if yes: go to 4, if no: go to 7)
4) Is the dwarf in a position of authority? eg: giving mandates and demands? (if yes: go to 7, if no: go to 5)
5) Is there a dwarven caravan present and about to leave? (if yes: go to 6, if no: go to 7)
6) The dwarf in question leaves, bringing any nonadult children and any unhappy spouses with them.
7) The dwarf stays.