... Another issue is some lenses just struggle with focusing against a strong backlight which is what you're essentially doing.
A full moon is not backlit. The moon is being lit by the sun infront of it. If the moon was backlit, the face of the moon we see would be in shadow.
I know that. But that's not how the camera interprets it. The camera sees it as light coming towards it, hence the same as backlit.
That's not what "backlit" means. When the sun or primary source of light is
behind the subject and
in front of the camera, the subject is said to be
backlit. Another way of thinking about it, is that the subject is between the primary light source and the photographer. There is a potential the subject will be seen in silhouette. Being backlit,
the side of the subject facing you and your camera appears to be in shadow. If the primary light source is especially bright (e.g. the Sun), glare from that source can wash out or add unwanted flare artifacts to a photo. It can also look pretty cool. Here's an example of a backlit Moon as a photo subject:

2017 "Great American Eclipse". The Moon is between the Sun and Earth. It is backlit and seen in silhouette.
In the case of a full or gibbous Moon, the Moon is frontlit or mostly frontlit. Earth is between the Moon and Sun. The Sun's light directly illuminates the lunar hemisphere facing Earth. The primary light source (e.g. the Sun) is behind or only slightly off to the side of the camera and photographer. Here's last night's frontlit Moon:

The craters along the right lunar limb can be described as "sidelit". The primary light source (the Sun) is off to the side. The shadows they cast are visible in the photo and add interest to the image...at least, to that part of the image. Most of the visible lunar surface - the left side - is totally frontlit. There is very little shadow to add definition or character.
During a new or crescent phase - the Sun rises or sets at the same time as the Moon (new), or shortly before or after (crescent) - the Sun can be said to be behind or mostly behind the Moon. In this scenario, sunlight will reflect off Earth's atmosphere and illuminate the lunar hemisphere in shadow. Especially during the crescent phases, it's pretty easy to adjust your exposure settings to capture the shaded side of the Moon, which is visible due to earthshine...sunlight reflected off Earth's atmosphere.

The thin bright crescent is directly illuminated by the Sun. The darker, shaded portion of the lunar surface visible in this photo is front illuminated by sunlight reflecting off Earth's atmosphere; earthshine.
The light is still in front of the lens shining towards it. That's how a camera sees it. And that's all I was talking about.
Portraits, landscapes, cityscapes, sports, street and other photos made during the daytime using ambient sunlight as the primary source of illumination are mostly frontlit. Just as when photographing a full Moon, sunlight reflects off the subject, is collected by the lens and focused on the sensor to make an image. The subjects in this scenario are not in any way, shape or form, backlit. These are frontlit subjects. For example...
Here, are a few examples of backlit landscapes with the primary light source behind the subject, the subject in silhouette or the light source visible in the photo.
No different than taking a flashlight and putting it between you and the camera. Just for fun, throw a subject between you and the camera. The source of light location is the same, in front of the lens shining into it.
If you were making a photograph of the flashlight shining into your lens, that's not a backlit subject. Being backlit refers to a subject illuminated by an outside source. The flashlight is the light source and is emitting light directly into the lens. It's neither frontlit nor backlit. It's the source.
Turn the flashlight around and shine it onto a vase of flowers on a table. If you make a photograph of the flowers, they are frontlit. While the light source is not "behind the camera," the light source is emitting light in the same direction as the lens is pointed. Light reflects off the flowers and vase and enters the camera lens. This is a classic frontlit subject situation.