Last night (actually, very early this morning) mechanicjay generated and installed new Let's Encrypt certs for our servers.
I made a quick check and everything seems to be in place. The old certs were due to expire right about now, so if you do have any issues, please pop onto IRC (preferred) or reply here and let us know!
No such API on BIND? What version are you running that doesn't support TSIG? That is the standard way to do this, after all. Just generate a TSIG key and restrict its update policy to TXT records for _acme-challenge.soylentnews.org.