I seem to have a gas leak from this part of the regulator but have no idea how to fix since it doesn't seem to be able to be tightened. Any pointers would be appreciated!
That's a 742 model. I have the two-body version. It's my favorite regulator.
I took a close look at mine and the rear section you circled is the automatic pressure relief valve. If you look through the holes you can see the spring inside. That section is apparently not serviceable as it isn't even included in the exploded parts view. Makes sense that they don't want users mucking with something that could kill them
As it's leaking, at the very least it needs a rebuild. There are two kits for the 740 series, 7740-15 for regulators built up to October 2006, and 7740-19 for regulators built after October 2006, and they are widely available (Midwest has both for under $15 each). But if the problem is within that PRV you might be out of luck with regard to fixing it.