I just wanted to update this further to point out how much of a mess Dreamhost's nginx support actually is.
As it happens, simply disabling supervisord isn't enough, as the nginx init script won't detect this, since all it does is queries a PHP_SUPERVISOR variable, which is actually stored in /etc/default/nginx, which must be manually changed as well in order to switch nginx over to using the ~/.php-launcher location as expected.
This means that creating a VPS admin is in fact mandatory, at which point it is easier to just change /etc/supervisor/supervisord.conf, or change the default PHP version by redirecting /dh/cgi-system/php.cgi, but then the whole thing is so messy that it's hard to know which option is going to ensure that updates won't break things and put us back to a discontinued PHP version!
It's just a complete and utter mess; either the .php-launcher method should be supported as standard, or the control panel should provide a means for safely setting the PHP version, we shouldn't need to create a VPS admin to change basic settings, and certainly not when Dreamhost has had years to get its act together. I mean, you guys even use nginx for your own site! So why then do you provide your best support for Apache, especially when its spastic memory consumption is just about the worst thing imaginable for hosts with fixed memory restrictions.