This question already has an answer here:
If I am davening at home and it would not be disruptive to others, is there any reason I might be permitted to say the Amidah out loud--for example, if it helped me with my concentration or orientation to G-d?
I found a discussion on the second half of the page here, which includes mention of the original Mishnaic source that one should daven the Amidah silently. However, this discussion seems to have some problems; it was hard for me to pick up a normative conclusion (other than the guy's opinion) from it. Also, I would like to know if one could pronounce the Amidah in a relatively normal speaking voice, which is not addressed.
My instinct is that doing so is not prohibited at the strictest levels, since some kiruv minyanim, and perhaps Karlin Stolin, daven the Amidah out loud.