[craigyb]

The higher the resistance you can use the less power they will draw and the less heat they will generate.

A bulb shows dead short as it's when it heats up that the resistance builds.

As you now have 2.7, 5 and 10 ohm resistors you can have a little play

2.7 + 5 in series will give you 7.7 ohms, try that to see if the bulb failure goes out.

These resistors are designed to be bolted down to a metal surface to help dissipate the heat