Please say which version of Eagle you are using.
Here are some ways for 5.11 in addition to what you already mention.
1) Outline with the Group command (dotted square icon). Click on the Change icon , select width, and select the width you want. Now, with the cursor outside the area, Right click and select Change group. If you click on the Polygon before clicking on the Group command, you can outline a polygon instead of a rectangle, then go through the change dialog.
2) Select the Group icon. Then press CTRL + SHIFT together and Left click on the traces you want to change. That adds trace segments for the whole signal/net to the Group. You can add multiple signals or just one. Click on the Change icon , select width, and select the width you want. Now, with the cursor outside the area, Right click and select Change group.
The second method, while a little more complex, is probably more useful as it is signal, not geometry based. The critical steps are explained in Help under Change and Group.
John