Well, it turns out (by experiment) that you can do this, with a registration-only account at Dreamhost, by using a free account at Cloudflare as your DNS zone file editor.
The steps are,
(1) add the domain to your Cloudflare account (Cloudflare will ask you to create "at least one" DNS record before accepting the domain, so I wrote in an arbitrary TXT record at this point)
(2) go back to Dreamhost and point your domain at the nameservers that Cloudflare tells you
(3) create a free Google Apps account for the domain, and verify your ownership of it by choosing "edit DNS" as the verification method, adding the TXT record which Google then specify to the zone file in your Cloudflare account
(4) go back to Cloudflare and add the MX records needed for Gmail.
Gmail is then up and running on your domain.
(Maybe if I had done these steps in another order, they could have been made even more minimal: the "at least one" DNS record which Cloudflare wanted me to add could have been the TXT record which Google asks me to add, or the MX records.)