I want to remove edges between two boolean-joined meshes as shown in the images below.
Honestly, I can only think of manually adjusting the verts to fit, or merge them. For merging verts, just select the edge loops on both parts, click on the merge icon on the bottom, and say S (scale) Z (locking z axis) 0. A way to use both methods, is to select a bottom vert on the top object, and the adjacent top vert on the bottom object, and say S, 0. Kinda tedious though.
Hope this helps.