How should I pronounce "Worcestershire" as a rhotic English speaker?
Solution 1:
Merriam-Webster (usually a good guide for rhotic US accents) gives \ˈwu̇s-tə(r)-ˌshir, -shər also -ˌshī(-ə)r\. The OED doesn’t give a rhotic alternative at all, just /ˈwʊstəʃə(r)/. Checking a few random other sources, I can’t find any suggesting that the first r should be pronounced.
I’d guess (fairly confidently) that a rhotic BrE speaker would say /ˈwʊstərʃər/ or /-ʃɪər/. Using /-ʃaɪər/ (Merriam-Webster’s \-ˌshī(-ə)r\) for the suffix -shire is strongly marked as an Americanism, to my ear, though I don’t know a source to back this up.
Solution 2:
I'm from Worcester, I was born in Worcester. Common Worcester is a hybrid dialect of rural West Country with a substantial hint of Brummie/Black Country. Locals including myself naturally exaggerate R's or include invisible R's at the end of many words. The prenounciation for locals and yourself should simply be 'Wuster'. (Wuss-ter) 'Wustershear'.
Easy. Simple as that.
Solution 3:
The pronunciations reported by the NOAD are /ˈwʊstərʃɪ(ə)r/, /ˈwʊstərʃaɪ(ə)r/. Having a friend who lives on Long Islang, I am used to the first pronunciation.
Solution 4:
The 'R' in 'Wuster' isn't so exaggerated but it could well be depending the individuals tone, if he/she leans more to the south (Herefordshire/Gloucestershire) or north (Birmingham). A typical example of exaggerating and including the 'R' would be "did you" and "did yerr" and "never" would be "neverr" using a rural twang. To people north and south of England while at University they thought of me as an especially lazy Brummie/Black Country talker and a local to Wolverhampton even though I live in Worcester City. The Worcester accent could be considered a lazy one in the sense we come across to people that we could probably formalise our tone if required and stop shortening words. "But it 'ent' that easy." 'Ent' for example is a local word I've not heard used elsewhere in the UK, it's used in our dialect for; ain't, isn't, hasn't (as if any of those words need shortening).
Hope this helps and apologies for my lack of IPA.