I found an interesting(ish) paper (
pdf) which did some analysis of the Corpus of Spontaneous Japanese. Apparently this is mostly people giving academic presentations and similar sorts of 'layman's public speaking', so by no means incredibly informal.
In this corpus, in adnominal form いう was pronounced /yuH/ more than 92% of the time, and the next highest variant was /yu/ at about 7%.
In adverbal form (ie renyoukei, masu-stem, or いい) 82% of the time it was either /iH/ or /iQ/, whereas /i/, /yu/ and /yuH/ were all small-number also-rans.
(The pronunciation indications are from the paper; H is 'long vowel', Q is the っ stop and the rest looks like standard kunrei-shiki romanisation.)
Which seems to back up what I had previously thought, ie that pronuncing いう as ゆう is completely standard, whereas pronouncing it as-spelt is very rare (plain form only; other inflections are not affected.)