I have some time sensitive emails I am triggering through the REST API messageDefinitionSends resource. however, I have noticed they linger around in the queue for a while before sending. I saw with the SOAP API you can set the priority. Is there a way to do that through the REST API or somewhere else in the interaction or email?
Trigger Priority is an additional per-email charge that has to be provisioned. You'll need to contact your SFMC rep.
Reference: Triggered Emails Guide -> Priority
So when you pay for priority sends, and it is activated in your account, it auto-magically shows up in the Triggered Send definition UI. Now that wasn't so difficult was it? :)