While I'm thinking about it, perhaps I should purpose a new type of demigod. Lets call them builders, crafters, or better yet, artificers. These "artificers" will support the war effort by building structures, crafting special equipment and making them available for use by creeps and other demigods, and making special stuff for themselves for when they meet other demigods in battle.
1) Building structures: These demigods can replace lost towers, and creating new ones at tactically significant areas. These are not the temporary ones the rook makes, but rather the kind that remain standing until destroyed. Other buildings might include additional healing crystals (weaker versions), and shops. Stuff on sale might a limited selection of the weaker stuff at the base, or some of the stuff these demigods have been able to make themselves.
Giving some thought on how this would work, an artificer might first create a temporary building. From there, it would spend time, energy, and money to make these temporary structures permanent. These structures might start out weak at first, so this demigod might need to do additional work on the given structures to upgrade them. Given enough time, an artificer may be able to fully replace damaged defences, or make better, upgrade existing defence beyond what they were at the beginning of the game, or even build a new base of sorts some place on the map.
Alternatively, these artificers may need to make a certain base structure first before it could start making other structures. This base structure would allow for the construction of other structures within a set radius (think zerg creep, or undead blight). In addition to allowing the construction of other buildings, they might even empower nearby structures. Of course the radius, and the power of the buffing effect increases as it is upgraded.
2) Map resources: Since these artificer demigods would make things, it might be appropriate to have certain resources on the maps to be capturable (flag capture). When a side has control of certain resources, the artificers of that side can produce new equipment, items, structures and other stuff. With salt peter's (for gunpowder), these demigods could provide some creeps with guns. Adamantine could provide stronger armour and weapons.
Of course, the type of demigod would influence the stuff make able, and their effects. Using the same resources, an alchemist demigod would make guns, while a necromancer might make exploding creeps.
3) Combat: Artificers being crafters would not do as well in combat as assassins for similiar reasons why generals would not. Being crafters, and maker of things, an artificer would probably require some time to build up resources, and other supplies before they can properly equip themselves. This equipment might change the nature of their abilities. An alchemist might normally have alchemist's fire for one of their abilities, but with the resources to make explosive, the alchemist might replace his alchemist's fire with alchemist's bomb, or even with a rocket launcher.
P.S. I did read a previous journal about wanting to keep guns out of this game. Any mention about that stuff was merely used to make a point.