Spoke to a rep from Vanguard, who made some calls and determined that Vanguard mutual funds DO distribute 100% of income - so they would qualify as income transparent offshore funds. I suggested they should publish this information for the benefit of UK resident investors in their mutual funds.
As nun found, some of the ETFs have undistributed income, so ETF investors should check the Schedule of Taxable Amounts linked above.
The Vanguard rep also passed along some additional information provided by their advisor department, summarizing various sections of the Investment Company Act of 1940, which is foundational to US securities regulation. All mutual funds and other Regulated Investment Companies are required by law to distribute at least 90% of income. However, they are still subject to a 4% excise tax unless they distribute at least 98% of income, so in practice most mutual funds are likely to meet or exceed the higher figure in order to avoid the tax.
I personally don't have any money invested outside Vanguard, but anyone who does is urged to ask these questions of their mutual fund company and report back!