What you are asking for is an orthographic view of a very wide, very tall three dimensional subject that can be taken from a relatively close distance.

Theoretically speaking, the most elegant way to do this would be with a linear motion scan camera, a/k/a parallel motion scan camera, such as those used for aerial or satellite ground surveys. Obviously, you'd want a wider angle of view and much shorter focus distance than is typically the case with aerial/satellite photography. Something more like the digital scanning back large format cameras used for art reproduction would be closer to what you need.

The camera scans one vertical line at a time as the camera moves horizontally with respect to the subject or, as is sometimes the case with much smaller subjects, the subject moves relative to the camera as the image is scanned one line at a time.

The camera would need to make several horizontal passes at various heights. The length of each pass would be determined by the width of the forest that you want depicted on the wall mural. Each pass would produce a long strip image with limited height coverage. The collection of the strips could then be stacked vertically in the way panoramic photos are created.

It wouldn't be perfect, but the minor amounts of perspective distortion would all be vertically oriented, so not very noticeable with trees that are much taller than they are wide. It wouldn't be cheap, either. Digital linear motion scanning systems are prohibitively expensive, as is the computational power needed to process such images.