I was just reading a bit of documentation–the RFC in fact–for SRV records when I had to stop and read the same sentence a couple of extra times because it was so unclear the first time. Here it is:

Name
The domain this RR refers to. The SRV RR is unique in that the name one searches for is not this name; the example near the end shows this clearly.

I did a bit of a search around and I found a site called Debian Help that had this to say on the topic (emphasis mine):

name
Incomprehensible description in RFC 2782. Leaving the entry blank (without a dot) will substitute the current zone root (the $ORIGIN), or you can explicitly add it as in the above _http._tcp.example.com. (with a dot).

Oh well. It seems I don’t need it.