Try focusing on your breath, and disregard your thoughts instead of trying to actively block them. (This is some kind of Buddhist meditation whose name I can't remember.) It took some practice at first, but it usually (not always, for some reason) works for me. (Another idea I read somewhere is counting your breaths, but after a while I practised that , I was able to count and think about something else at the same time.)

I can shut down my internal monologue by concentrating on some sound from the environment (effectively replacing it).

Did you try really hard? I have succeeded on the first try; just didn't like the result.

I didn't really learn it, I just had a few reasons to block some thought direction (impression rehashing gone harmful), and so learned to block. The basic idea is like that: get any idea you can tolerate - imagining literal word "CENSORED" cast in concrete is a fine starting point. When you notice the "blocked" thing occurs, think the "showstopper" thought. If you have multiple background attention threads, fill them with independent copies of the showstopper. Once this becomes nearly a conditional reflex, the blocked thought will wear away because it is never reinforced in actively operating memory. It will stay in passive long-term memory, of course.

A close technique - replacing any attention thread with something easy to shut down and shutting down - allowed me to shut down inner monologue. I got some performance-boosting consequences out of that. While it is hard to say how it felt in real time (I did this precisely to have some excessively repetitive things done while minimising the experience of doing them), retrospect memories of this are quite uncomfortable.

I don't use an internal monologue for normal thought, only specific kinds of thinking, especially when I want to remember my thoughts very clearly.

I'm not sure what you guys mean by shut it down. Can't you just stop using it?