," how many issues would it take to be prudently diversified if one were attempting to put together a high-yield portfolio? (as opposed to an investment-grade one, where, presumably the threshold would be lower). "

Agreed.
If I wanted to participate in the debt of emerging markets, surely the way to go is a fund. The alternative is unthinkable.

Here's some numbers you already know, but let's look at them:

T. Rowe Price's high yield fund: 30 day yield 8.98%
Vanguard's high yield fund, 30 day yield 8.68%

T. Rowe Price's "US Bond index fund": 4.99%
Vanguard's total bond fund: 5.68%

We know Vanguard has lower expenses. Clearly T.Rowe Price is digging deeper into "junk" to get the higher yield.
It is not clear to me why there is so much difference in the bond index funds.

We see that for Vanguard, the high yield fund is paying 3% more than the index fund, and for T.Rowe Price, it is paying 4% more.

We accept a non-zero default rate in order to strive for a higher yield. If the default rate is less than the premium in interest, we may be earning a little more by accepting it. To get a 3% default rate, I'd think you must have 33 bonds, and preferably more.
The problem, apart from trading costs, is to find 33 different bonds you think are mis-rated. You will get each one by observing what the stock is doing, calling the company for a 10K and an annual report, etc. Then you hope to hold the bond for several years. To repeat this process more than 30 times....yuck! Let the fund manager do it, IMHO.
If I buy a bond issued by General Electric or IBM, I think I know what problems the industry is facing and can be in my own mind quite confident that the company will be around when the bond matures. My portfolio of investment grade issues has been built up over more than a decade; I own stock in most of the issuers of bonds I hold, so in that way can keep some tabs on the companies without making a lot of phone calls. In 1993 most of the bonds I then owned got called, and it looks like this year will be another dose of the same. What was once a portfolio I thought was adequately diversified is now...er, 6 corporates? Finding appropriate substitutes is tough. Last time I switched from corporates to municipals; this time I started out getting preferreds, but now have pretty much thrown up my hands even at those. What remains is go for a junk fund, just buy stock, or take the cue from Charlie and look at emerging market bond funds....and then there's the folks who would like to sell me oil-drilling partnerships...
It isn't gonna be easy being retired! If you can survive the low interest rates and the bonds getting called, then there will come inflation again rearing an ugly head.
Best wishes, Chris