My take on this:
General question: No, that's not strictly outside the bounds of Lawful Good, as an isolated incident and/or a moment of poor judgment on the character's part. I'd frown on a LG character regularly handling things in such a fashion. Threatening innocents should be very much a last resort, and the first course of action should ideally have been something else. Mass enchantments, Diplomacy over Intimidate, trying to scare them WITHOUT the threat of death, etc. The character's actions were not LG, but not so severe (alone) as to merit an alignment change.
Specific instance: I don't think your GM was in the wrong to change your alignment, because I get the impression it was NOT an isolated incident, and as you indicated, the character was already acting more LN.
Lawful alignments are quite willing to impose their views on others even if they are not willing. So saying the lawful good character cannot use intimidation before exhausting literally every other option is kind of silly. Lawful alignments are also not that interested in freedom that is a chaotic hang up. Lawful societies have rules and punishments for breaking those rules. How is this any different than making a law that says if you steal you will be put in prison, and if you resist any force necessary to take you will be used to apprehend you?
You are also advocating the use of magic to impose your actions on another person as being less evil that threatening a person. I would say that using magic to force someone to do something is a lot worse than using intimidate. Many people think that using magic to control someone’s mind is actually very evil.
Also note that the original poster did in fact try all other options.