Your thoughts on connecting multiple leds in parallel and series
You do have to place the series resistor in each branch, even if the LEDs are all the same. The internal resistance of a LED is so small that a minute difference in voltage will cause most of the current to go through one branch (or hardly any, depending on whether the voltage of the one LED is lower or higher).
A constant current source is not a good idea for the reasons you mention: if one branch fails the others will see 33% more current. Fuses may help, but there's some tolerance on their nominal breaking current, so be sure that they don't break at 750ma and will break at 1A. Once the first fuse has gone the others will follow fast. I would recommend a constant voltage source, though.