If you take a look in the API reference it would certainly look like you can send to more than one account at a time per request.
SendEmail requires an argument of 'Destination' of type 'Destination'.
Destination has three properties: ToAddresses, CCAddresses, BCCAddresses - all are of type "string list".
If you look at the example requests in the Developer Guide, you'll see it specified the destination addresses as an argument similar to:
&Destination.ToAddresses.member.1=allan%40example.com
I'm going to go out on a limb and guess for a 'string list' they're expecting multiple addresses in a format similar to:
&Destination.ToAddresses.member.1=allan%40example.com
&Destination.ToAddresses.member.2=other%40example.com
&Destination.ToAddresses.member.3=asdfq%40example.com
...
&Destination.ToAddresses.member.1000=final%40example.com
I actually stumbled across your question looking for answers to some of my own questions about SES - as of yet the docs are complete enough to use, but not always terribly helpful - you often have to make some fun inferences to get answers - just a fair warning for you!
Cheers!
Edit: One other thing that might be possible I pulled from the quote you posted in your self-answer:
either by modifying the software to directly call Amazon SES, or reconfiguring it to deliver email through an Amazon SES SMTP relay as described above.
If you set up your own SMTP server, and just have it relay/forward through SES, that might handle your queuing/etc. You can just shoot out a few thousand e-mails and your SMTP server will handle queuing/etc before it hits Amazon.