Good to see someone enjoying reading books about the Welsh language (as I do!), but important to stress here that “eisiau i fi” is perfectly fine and used.
Just because forms do not appear in certain books that someone possesses, does not mean that they do not exist and are not used (locally, dialectically, or in “high grammar”). Any more than because some words don’t appear in a particular dictionary they are not “the right Welsh word”, concerning any style of Welsh.
There are very few grammar books and dictionaries which give you the whole picture, whether considering “dialect” or “literary” grammar.
“Mae eisiau i fi” is fine.Certainly not wrong.
One quote you use describes it as “ffurf lafar”, but this does not imply improper. It is fine. My reaction to that is that is it backs up the use of “eisiau i”, rather than being “close, but not quite”.
My family in Carmarthenshire would certainly use " chwant bwyd arana’i" for being hungry rather than starving. The use of “chwant” in that case does not, as far as I can see, imply something stronger than it would were they to use eisiau in that case.
This is a really complex issue, but also very simple and easy to get through.
“eisiau” is a word which covers both “want” and “need”. Other words in various areas cover want/need in their own way. There are several ways, all equally valid of ‘grammatically’ using the word eisiau in a sentence.
How someone uses it, whether the way they use it determines the meaning or not, what other words they use alongside it, differ from individual and individual. This involves differing from area to area and situation to situation.
This may sound offputting, but it simply means if you use any one confidently, you will be understood, as the context will make it clear what you mean!
It is good to see someone enjoying looking in books about the Welsh language (as I do, tremendously!), but when you say
though I found both books and Welsh online to be fascinating, useful resources, I only really understood what they were saying (what exactly they were referring to, what type of language, and, quite frankly, whether they were right or not!) when I started having conversations with native Welsh speakers.
I only mention this because you say “eisiau i fi” is wrong. I know you say “as far as you know”, but I wouldn’t want anyone reading this thread to come away with the impression that “eisiau i fi” is wrong.