Ignore the zero fret, as long as the octave fret is halfway (OK there is an "end" adjustment) between the zero fret and the bridge, then the guitar should be tunable. The most probable reason that you were having problems, was that the strings were not sitting in the nut properly (had you fitted heavier ones ?) and therefore not touching the zero fret. All you should have needed to do was to file out the slots in the nut.

I prefer a guitar to have a zero fret as this is much less likely to wear down than the slots in the plastic nut and means that the strings follow the curve of the neck more accurately. It also ensures that the sound you get between a fretted and open string is of a similar tone as they are both resting on metal.