I think @roux is generally right, curries are like mexican moles, they have lots of spices and are fairly complex. But I do think there are some short-cuts.
The most important components in a curry are sweetness, creaminess, heat, citrus, salt, and depth. I don't know if by simple you also mean you want to use common ingredients, or just 'few' ingredients. This is what I would use if I only had common ingredients:
Coconut milk, cayenne pepper, onion/garlic/ginger, lemon/lime juice, salt/pepper, sugar/honey. I'd also add basil/cilantro/jalapeno for green, tumeric/cumin for yellow, ketchup/tomato paste/chili powder for red.
If you have them, the traditional ingredients you're trying to replicate are lemongrass, lime-leaf, red or green chiles, and fish sauce (or soy sauce).
First, start your Thai coconut curry sauce in a separate pot (i.e. the coconut milk and later the seasonings; no meat , no vegetables, etc.). Make sure to shake the can of coconut milk before opening to ensure it is not separated. Add 1/2 the can to the pot. Bring to boil, reduce temperature and allow the mixture to reduce to almost a paste like texture. This will allow the coconut flavors to intensify, and give you a thicker starting point.
The key is to reduce some of your sauce before cooking everything else; if you attempt to reduce your entire sauce with the vegetables, they will overcook because the process takes too long. Once reduced, add the other 1/2 of the coconut mixture. You end up with a very silky, smooth coconut sauce. Afterwards add your curry paste, fish sauce, sugar, Thai basil etc.
Best Answer
Disclaimer: I have no experience with low FODMAP diets. But it seems quite a challenge to make a Thai curry without garlic or shallots in any case!
In Thai cooking, you typically want to have very strong flavours, and a balance of the basic flavours: bitter, sweet, salt, sour, and umami. So perhaps your problem isn't so much having a strong bitter taste (which isn't appreciated as much in western cuisine as it is in Thai cuisine), as a relative lack of the other basic tastes?
I would suggest that you may be missing out especially on salt and umami, because you haven't used any fermented fish sauce (which is typically very salty) for seasoning, nor fermented shrimp paste ("gapi", which is very umami) in the curry paste. One teaspoon of salt is not very much; in commercial curry pastes you may find as much as 25% salt.
Other things that come to mind (which may or may not be relevant to your issue):
Don't use lime juice in the curry paste; but do use a bit of lime zest. It's fine to use lime juice for seasoning while cooking the curry, though. I typically use a bit more than one teaspoon, perhaps two or three. But it all depends on the balance of the dish: as a rule of thumb, add (palm) sugar for sweetness, fish sauce for saltiness, and lime juice for sourness, until you can taste all basic tastes, without any one overwhelming the others.
Don't include the coriander leaves and top part of the stems in the curry paste, only the roots and lower part (about an inch) of the stems. You can use the leaves to garnish the dish.
Don't use spring onions in the paste, as they make a poor substitute for shallots; they're also better used for garnishing the dish.
Use galangal instead of ginger, if you can find it (if I can't get fresh galangal, I won't even bother trying to make my own curry paste).
Hope this helps!