Here our blood oranges are grown in two place in Sicily. Both palces are pretty hot during summer but they can get quite some cold during winter. The frost is mainly generated by orography, being generated inside the island, on the mountains, and slowly falling towards the sea a night.
The production of blood oragnes there follows strict rules, imposed by european community, wich dictates the varieties admitted to be labelled with the name "sicilian blood oranges" (Arancia rossa di Sicilia). They are three (but only some clones for variety are admitted): Tarocco, Moro and Sanguinello.
I find interesting that all those varieties become blood oranges if you expose them to the right environment.
For the production of blood oranges here the rules admit only 4 kind of rootstock: Sour orange, citrange troyer, citrange carrizo, and poncirus trifoliata.
I dunno if one of them would do fine in a more tropical climate, but i'd say that a sour orange should work fine. The poncirus is pretty hardy, as far as i know, so maybe it isn't the best bet.
For my likings, i prefer navel oranges. When i eat a fruit i like it SWEET. Blood oranges are tasty but i have hard times finding good ones, and a navel oranges is way easier to find and more sweet, as far as i have encountered. If someone knows some citrus even sweeter please tell me, but i don't count on it.