Accent is a systematic substitution of sounds for other sounds that you would normally expect (“normal” here depending on where you’re from and what you learned, etc. etc., the usual disclaimers…)
This is really closely related to Giles and his theories about simultaneous interpreting and brain load. Essentially — and from experience I think this is correct, plus it’s so simple it seems intuitive — you have only so many brain resources to understand a message (in interpreting you must also output, but for this example it’s just comprehension). Listening to normal speech, you can use those resources to understand the words and think about the meaning. Listening to an accent, some of the resources have to be devoted to “translating” from the accented words to the form you know, so there are fewer left to listen and understand the message itself, and you’re prone to fall behind and get lost.
So you can potentially attack any accent issue just as you would attack any other issue of teaching language varieties — expose the students to the new variety at a speed they can understand (slowly) while pointing out the systematic differences that make up the accent. For that, if you are a reasonably good imitator, you could model the accent yourself at a very slow speed at first.
Part of the challenge of the Indian subcontinent accent is the speed and the feeling of having smaller or no space between words. So vocabulary study (and having really automatic responses to vocabulary words, rather than needing to decode) is very important there. If the listener needs to “decode” the accent (translate from the Indian accent to the phonetic form he’s used to) and then use more time to decode the word, he will fall behind due to the speed, and if he misses enough language, he won’t be able to understand no matter how good his grasp of the accent.
I’d make a list of the major features of the accent and point them out, then devote some speaking/listening time to them interacting with you using that accent in increasingly fast ways. And, of course, keep Googling to see if there are some materials out there for when they have the idea but need authentic practice. (Or you could just have folks in the US record their customer-service experiences…)
This is where it’s important for teachers to have a working knowledge of Phonetics. Some of us can imitate accents pretty well, but can’t tell a student exactly which sounds are changed or how. Knowing Phonetics is a big help in getting students to pronounce things correctly, rather than relying on trial and error or luck or their innate imitation skills.