You can do some cool stuff with just an iphone and a telescope. Computational photography is finally starting to make it's way to full sized cameras as well.
The good thing about bird photography is your equipment is also great for moon photos.
If the moon is out tonight I'll try it on my phone and post the results with the settings I used. It looks like my phone doesn't let me control aperture but should be able to still get a good result just using shutterspeed and ISO controls.
A lot of smartphones let you turn on the manual settings for the camera. You should be able to get a decent shot if you directly control the shutterspeed/aperture/iso. That's Pro mode for Android. idk what the apple equivalent is.