Time for speech therapy?

Hi! My three year old, in my opinion, is very behind in pronouncing words, both in English and Italian. At the moment, he's using English more because he's been home with me for the past three months but was taken care of by his Italian grandmother during my work days, so he totally understands both languages. I'm not concerned about the words he's using because I know with my first son, he totally caught up with his Italian when he was three and started Pre-K, which my youngest will start in two weeks. I'm more concerned about how he doesn't say many last consonants, middle letter combinations, once he decides a thing or person is called a specific way, that's IT, he'll call it that forever... And although it is endearing to hear him call Aunt Milena Ya-ya it's also frustrating that he refuses to call her by her name.

I've brought up my concerns with the pediatrician for about a year now and he said to wait until the child was three. He has gotten better in the past few months but mostly in adding new words, pronunciation is still quite limited. I have an appointment in a week with the pediatrician for a recommendation for a speech therapist but in the meanwhile is there anything I should be doing? He is surrounded by English, I read to him nightly and often during the day, when he makes mistakes I gently correct and repeat... Anything else? I find that I end up having to translate for him not only because he's speaking English but often because he's speaking 'Noah-ese'

Regarding speech therapists. Has anyone had experience doing it in the majority language and it being effective also in the minority? I assume we'll have to go to an Italian one and the most I can hope for is that they are open to the child being bilingual. I am however a bit nervous that they won't catch on to a lot of the mispronunciations since they're in English...

Any advice is greatly appreciated! Thanks