I want to close gaps in a model to make it printable I'm trying to learn Blender through a project: preparing a model for 3d printing.
This particular model has a big problem: it's non-manifold. In a big way!:

As you can see, as the model was created to be seen from a front view, it didn't need to have a body under the longcoat. It's up to me to close that big gap so it prints, melding the legs together with that in the process.
I tried creating a plane, intersecting at the height I calculated it would touch both legs and the coat.

I made a boolean modifier, with union. My reasoning was, once the boolean is complete, I'll be able to select the exterior section of the plane, that will be cleanly cut by the exterior silhouette of the model...

However, that is not the case. The plane kind of becomes bugged out, and the area of the plane that sits right where I want it is not really separate from the rest.
How would you solve this particular problem?
The problem seems to be that you have way too many vertices it would be expected that the plane makes many triangle faces and looks very buggy.
A way to approach this is by not using a plane at all. Try hiding everything that is not the underside of the long coat (bottom of the torso if you will). Then you can switch to bottom view by pressing Ctrl + Numpad 7 and box selecting (B) all the faces you see. Afterwards you can extrude these faces down and flatten them on the Z axis with S + Z + 0. This should create a flat surface that you can drag to a desired height.
P.S. If you don't have vertex groups and are finding hiding everything difficult, you can also circle select (C) the underside faces manually.