My suggestion would be that you simply ensure that your English pronunciation is clear to everyone you interact with. I don't think it would be a good idea to strive for the pronunciation of a community of speakers of which you are not a member. The 2020 school syllabus in Singapore "continues to underscore the teaching of internationally acceptable English" - not American English, British English, Singaporean English or any other variety. Excellent German speakers of English tend to have a slight German accent; when you listen to highly proficient Russian speakers of English you can usually tell after a few minutes that they are from Russia. In your case you may sound Indian. Well, that is your identity and you should be proud of it. As long as someone's spoken English can be easily understood when, say, speaking at an international conference, there is absolutely no need to strive to sound American or anything else. Leave that to actors. Be yourself, that would be my advice.
I believe that improving your accent and pronunciation can be beneficial, but it should not be the primary focus, especially when you are first learning English. The key is to ensure that your message is delivered clearly and understood by your audience. As you continue to practice and immerse yourself in the language, your accent will gradually improve. However, attempting to perfect your accent before achieving basic fluency and comprehension can impede your progress. In other words, your approach of prioritizing intelligibility and then refining your accent as a secondary goal is the most practical and effective way to develop strong English communication skills. The ultimate goal should be to express yourself clearly and confidently, not to sound exactly like a native speaker.