Just an update for folk who may find this in the future…
It turns out that my host mistakenly told me that my server cron was enabled but, upon looking at the Support tab in the Offload SES plugin, I saw that WP Cron was frustratingly still enabled.
I have since switched from WP Cron (which, in my case, is rather overworked and possible held back by certain optimization and caching plugins) to a server cron provided by my hosting provider. Since doing so I no longer have any queue and emails seem to be sending immediately.
I hope this helps. Great plugin, easy to set up, and works flawlessly if your site is set up right!
