Mandarin pronunciation for  and Consider for example the words 很 (hěn) and 员 (yuán). I constantly hear each term pronounced in at least two distinct ways by native speakers. The issue is really the vowel sound in the finals.

Approximate to English, I hear 很 pronounced as either "mother hen" or "Attila the Hun", while 员 sounds like "innuendo" or "Are you honest?".

I've attempted to look up the "official" pronunciations through Wiktionary, IPA transcripts, Pleco dictionary, etc. but I keep running into discrepancies. So which pronunciations are standard and which are dialectal?
@DrunkenMaster's comment is right you will meet many accents of Mandarin. But there is a literally official standard of pronunciation in the PRC, tested by the 普通话水平测试. Set levels of performance are required for school teachers, local tv announcers, national tv announcers and so on. This is probably the most widely understood single accent -- even if no one in China speaks it perfectly!  

This explains why the charts in Ringil's answer to When is a 方言 a language and not a dialect show people all across China understand Beijing dialect better than any other except for their own regional dialect -- and in many cases understand it significantly better than their own regional dialect.  The Beijing accent is closest to the official one that everyone on China hears on TV.

I know no good source for official phonetic information related to the  普通话水平测.  But I take it you still want some good reliable, single source, to take as your speech standard while you learn.  Anyway that is what I want, as I think it is important to aim for good mastery of one accent as base, and other local ones if you like on the side or later.  That one should be the most widely understood accent (and the best received in business and academic circles if that matters to you).

After trying many different sources, digital and print, I suggest Yen-Hwei Lin The Sounds of Chinese.  It gives very careful and clear explanations, and recorded examples.  It does discuss variants of many phonemes.  But obviously no book is exhaustive on those.  And anyway at this point, to learn one reasonably authoritative accent for your own speech, go with the dominant version Lin gives for each phoneme.  

I will not repeat what Lin says about hěn, and yuán, but refer you to that book's full account.