[MP&C]

Heat from welding causes shrinking, so it's possible your proposed method ends up holding the panel in the "caved in" location better for you, as well as adding a dirt/rust trap.

The panel may need more outward crown in the area of the dip, in seasoned hands some strategic planishing would take care of it. Incorrectly applied, you would add too much stretch and significantly increase the size of the wave. It could also have some stresses that have been captured there due to shrinking from any welding that occurred. A wave could also be a sign of stretched metal, looking for someplace to go.

Basically, there are many defects it COULD BE, with different corrective action depending on what is there. It is much easier to send you down a more correct path once detailed pictures let us see exactly what you are looking at. If any oil canning is occurring, then perhaps a video is in order. One that would show the "easy to push" area and how it acts, and where the perimeter of the oil can is located.

There's a reason you can't get a paint estimate over the phone, same applies here for getting a more accurate recommendation. IMO the panel needs to be stable before any thoughts of filler. A flexing panel won't hold filler long...