@j_causby ,
There is a Get Terms (plural) API call, but you'll have to scan it for the one that you want. It does not work if you tack an ID on the end. It's List enrollment terms from the Enrollment Terms API. Depending on how your terms are created, it may not take long to get the needed term. The source code shows that they are sorted by start_at, end_at, and id, with the start_at and end_at fields being in descending order (reverse chronological order). For us and only three terms a year, we would hit the current term without having to mess with pagination.
I also like Peter's trick of doing a PUT; I hadn't thought of that. At first I didn't see why Peter said you had to know something else until I tried it. The reason was that you can't do just PUT without a payload, you have to specify something or it returns a 400 Bad Request message. What Peter knows about API and LTI makes me feel like a "C" student.
Another trick some of us use is to keep a local cache of Canvas IDs in our own databases. In other words, I don't need to query what's in Canvas for the term or course start for most things because I have that stored locally and use it for most things. An instructor can change it inside Canvas and open their class up a week early, but all processing with the SIS is determined by the dates on my local copy, not what the teacher does. For things that need to be portable so that other institutions can use it, I obviously don't have that luxury and have to look up things through the API.
As far as the dates go, there is a coalesce ran on the section date, the course date, and the term dates. The first one that is not null is the one that is used. So, if you're not specifying section or course dates, then it uses the term dates, which probably explains why the course start_at and end_at were showing up null. We only specify course dates on our end, except for a special section we put everyone in who hasn't completed the mandatory student orientation to Canvas. That shows them that they have the course, but won't let them into it until the complete the orientation.