Any advice on how to deal with the dripping run off without getting into a battle with the EC?
You only need to get into a battle with the EC if they refuse to do anything. A polite letter asking them to issue a notice to comply with the quoted section of the by-law, or explain their decision not to do so, might do the trick.
If they refuse to take action, you might remind them that they have a duty to enforce by-laws and that failure to do so can lead to action under section 232(2) of the strata Act.
This is not an unreasonable request so if there is to be conflict, that’s their choice and can be resolved through NCAT if they want to go down that road.
Otherwise, perhaps you could have a quiet word with your strata manager and ask them to issue the Notice to Comply – which they are empowered to do. The run-off pipe is there to allow water to escape when the balcony is flooded – it’s not there to provide a permanent escape for dripping water.