Is there a politically neutral Chinese term for Greater China that is acceptable to all Chinese speakers?
maybe "大中華區". most multinational corporations used this term to describe the regions you mentioned. 

such usage is correct, in context of nowadays, or recent decades. historically, taiwan was integrated into the chinese empire after ~1683. before that time, formosa was colonised by the dutch, spanish.

history of taiwan  

last, and most importantly is: how do you define "chinese speakers".

there're many ethnicities in "greater china" can speak chinese, they've their own cultures, languages and ideas of state / nation. so, "politically neutral" is, imo, unattainable.

it's better to seek a term that's vague, fuzzy enough; that no-one want to waste time and effort to argue its precise definition.