If you haven't already solved the problem with the other answer, here is a hack that should work. There are probably a lot of unnecessary details.
In the UV Editor of your .blend file, turn on UV Sync (1) and Vertex Select Mode (2). Then select the top row of vertices (3):
In the 3D viewport you will have this. I used Shift->Z to make it easier to see:
I put the 3D viewport into Front Orthographic view and selected all the edges:
The pressed Delete, but deleted Faces:
Select the top edge of what remains:
Shift->D to duplicate it. Press ESC to not move it. Then separate it by pressing P and choosing Selection:
Go into Object mode and choose the separated BezierCurve.002. Then Edit Mode, select the edge and E Z 10 to extrude a new section for the can.
Select all of what was just extruded and assign the Red Metal Material to it as it originally was:
Then select an edge and Mark Seam. Select all and for this unwrap, I used the Unwrap method:
It gives this result. You can select a line of vertices to see which is the top and rotate it accordingly, after selecting everything, if you want the top at the top:
In the UV Menu I checked Constrain To Image Bounds and moved the unwrap onto the image. I turned on Display Stretch:
Then S Y to fill the image:
If you want a bit of a margin around the unwrap just scale it in a bit.
In Object Mode you can join this new part to the base Ctrl->J