I would probably say this like:
Mi ne bezonas longan tempon por fari ĝin bone.
I think when the “to” before a verb in English can be replaced by “in order to”, it’s better to add the “por” in an Esperanto translation to make the meaning clear.
Some comments on your examples:
Ne necesas ke mi longe fari ĝin bone
This one is not correct because it has a subject with an infinitive (mi fari). It sounds more like you are saying that it’s not necessary to do it at all.
Ne necesas al mi longe fari ĝin bone
I think this one is a good translation but to my ear it would sound better if it was “por fari” because it’s not clear whether the longe is describing fari or whether it is the subject of necesas.
Ne bezonas ke mi longe fari ĝin bone
This has the same problem as the first one.
Ne bezonas al mi longe fari ĝin bone
I think necesi is the right word rather than bezoni. Bezoni is a transitive verb so if you want to use it you really need to make mi be the subject like in my proposal at the top.
Regarding the word order, I think putting bone at the end sounds the best, otherwise putting it before fari works too. The latter is the natural word order but putting it at the end changes the emphasis and I think it better matches the meaning of the English sentence.