from what I hear, he only does it three (or maybe four) times, all at the opening of the refrain “Lydia[r], oh Lydia” (but not on the next “Lydia, oh Lydia”; it’s just in the transition from the verse to the refrain.) He never says it as “Lydia[r]” if the following word starts with a consonant, but it just seems to me to be a flourish on the head of the refrain.
I did mention it, in the footnote. 
I wouldn’t say “Chinar” on its own, but I would say “I went to China-ron holiday” or “China-ris a major manufacturer”, because of the vowel. Writing it down looks funny, but it’s just the natural speech pattern for much of England (and, by extension, Boston etc).
No thread on rhotacism is complete without weleasing Woger!
Oliver Sacks spoke this way. “Bwain suwgewy”. I think it may be more of an upper-class affectation than a dialect.
While I associate “fun with 'r’s” with Boston, my most memorable example was when I was in grad school and a student from Connecticut asked me “Hey FtG, can I bowwow a quahtah?” Not an ‘r’ in the whole sentence.
OTOH, I had a co-author of a paper who was from Boston presenting it a conference and he’d say things like “The idear behind this is … .” Cringe.
The screenplay for The Princess Bride was adapted by William Goldman from his own novel of the same name, and in the book the clergyman is described as having an impediment that had become worse as he aged due to hearing loss.
What’s more, the specific way this character mispronounces words in the movie is taken from the book. The exact wording of the clergyman’s speech is slightly different, but he says “Mawidge is a dweam wiffin a dweam” on the page, with that spelling. So I’d be pretty sure the character in the movie, like the character in the book, is supposed to have a speech impediment and not simply a different accent than the other characters.