How can I break English L2 pronunciation habits?

I have a trick I use when learning another language: I speak my language (English) with a strong accent of the target language. That gets me into the feel, rhythm, where in the mouth I am making sounds, etc. Then I cut straight over to the target language keeping that feel.

I've been told by native speakers of all sorts of languages that I say words exactly like a native - with absolutely no detectable accent. Maybe you could try that.

I have had a similar problem when I was teaching German in Japan.

If the students are old enough you can explain to them that the phonetic pool of English is totally different from the one they have in Japanese, so they need to learn how to pronounce their words from scratch.

I spent about an hour teaching my student how to pronounce a word he never got right before and when it finally worked, he was really happy - also because he was instantly able to pronounce similar words correctly.

Another situation I had was when a student was able to produce the right sound already when combined with other vowels:

ich ("I" in German) echt ("genuine", "true")

acht ("eight") <--- my student always pronounced the "ch" as "h" here even though he got it right in the other cases.

So I made him say those words in a row "ich, echt, acht" to correct the "acht".

I realize this is pretty close to logpedics and speech therapy, but it does work in practise given a student who is intrinsically motivated to learn a language.