The correct exposure for the sunlit moon is about 1/50 f/8 at ISO 400.
The correct exposure for the copper-coloured eclipsed moon is about 2 seconds f/8 at ISO 400.
So if you want an image of the moon showing how the sunlit crescent blends into the sunset-lit eclipsed part, you'd have to take two shots at exposures 100x apart and merge in Photoshop afterwards. Fine, that's the kind of thing Photoshop is for.
There is a horrible technical problem, which is that the camera (particularly if running at f/13) won't auto-focus on something as faint as the eclipsed Moon. And it won't run long enough exposures in live-view mode to be able to see whether you're in focus; for the partial phase I could focus accurately on the illuminated part, but at totality everything's quite fuzzy. There must be an accepted solution to this - I suppose I should have pointed at a bright star and live-view-focussed there, but it was 3:30am and the Moon in a region of the sky without really obvious bright star.
Then we run into the fundamental problem. With the long lens and teleconverter, the moon comes out 2000 pixels across, so one pixel is half an arc-second near enough. Unfortunately, the moon moves across the sky at a rate of about 1.3 million arc-seconds per day (that is, all the way round the sky in one day), or fifteen arc-seconds per second, so in a two-second exposure the best you can hope for is sixty pixels of blur. I took a thirty-second exposure to demonstrate this:
That's if the tripod doesn't wobble. And with the very bright uneclipsed-moon in the frame you will see every wobble ... this one is the least-wobbly partial-phase picture I managed.
An actual telescope mount would be solid enough to hold everything still, and would have a little motor to rotate it to follow the motion of the moon; on the other hand it would cost more than the already-quite-extravagent birding lens, I would use it no more than six times a year, and it would take half an hour to set up at 0230 with sleep-befuddled brain. So with what I've got the right answer is probably to give up on filling the frame and go for something artier instead: