Not what you want to hear, but I don't think you'll find a good learning tool that doesn't require you to learn the script. I'm not a Hindi learner but I have quite a bit of experience learning other languages that use Indic scripts (mostly Thai), and I've seen quite a few people learn those languages with varying approaches to the script and varying degress of success.
The thing is that you have to have some way to write down what you are hearing / learning, and the only good way is to use the script that belongs to the language. Sure, in theory you can transliterate into the latin alphabet, but in practice transliteration systems are a disaster. For one thing they're inconsistent, but more importantly they wreck your pronunciation. If you write down the words of your target language using the spelling system of your own language you will end up saying them with the sounds of your own language. Some of those sounds may be similar enough for you to be understood, but none of them will really be the same, so at best you are locking in a strong foreign accent.
Quite a few people recommend using the IPA as a kind of stepping stone, but that takes time that you could put towards learning the script itself (and you're going to have to learn it one day...) You also have to bear in mind that each IPA symbol actually covers a pretty wide range of sounds. People will talk as if the IPA is more precise than other writing systems, but that's not the case at all. If you want to be precise there are all sorts of diacritics you can add to the basic symbols, but it's a fair bet that learning all of those would take you longer than learning the Hindi script.
If you take it a step at a time it really doesn't take all that long to learn a new script, and it gives you a much better foundation for learning the vocab, grammar - and above all pronunciation - of the new language.