Sorry, I shouldn't laugh but I did, because I can relate to "it's starting to do my head in". I'll be watching for replies with interest.
I don't know the answer of whether verbal stim or echolalia are the same thing. It's something I've just started looking into myself.
I have 2 sons, 6. Both have got developmental delay, both were slow to speak. I have ended up with one son who talks CONSTANTLY, I mean, he never shuts up! It's completely wearing, but he's not repetitive with it. It's just like his brain is full and he moves and talks all the time.
My other son (just referred for ASD assessment), has very repetitive speech. "What's this Mummy?". I'd reply. Two seconds later, same thing "what's this Mummy?" - referring to the same thing. Repeat ad-nauseum. Another one was "how many sleeps til.......?".
Best advice I was given was by a Behavioural Therapist. Answer the repetitive question once, or twice, but then change your answer if they ask again.
For example:
"What's that Mummy?"
"Its an apple"
"What's that Mummy?"
"It's an apple"
"What's that Mummy?"
"Tell me what you think it is! What colour is it?"
It took a while, but the repetitive speech has diminished. He still asks "set" questions, but knows what will happen if he continues to ask.