I think you missed that you have to modify the frame in the Envelope Address
style, not just in a document. When you modify the style, choose the radio
button for "New documents based on this template." Assuming the template in
question is Normal.dotm, that will cover envelopes created thereafter.
Again, here are the steps:
1. On the Home tab of the Ribbon, click the arrow below Change Styles in the
Styles group to open the Styles window/pane.
2. At the bottom of that window, mouse over the buttons till you find the
one that shows the ScreenTip "Manage Styles" and click on it.
3. On the Edit tab, choose the sort order to Alphabetical and scroll down
(or up) to Envelope Address.
4. Select Envelope Address and click Modify...
5. In the Modify Style dialog, click the Format button in the lower left
corner.
6. Choose Frame.
7. In the Frame dialog, change the vertical position (and size) as desired.
Note that by default the frame is formatted as Bottom relative to Margin. If
you want to leave it there (a good idea) and move it lower, then you need to
reduce the height.
8. After making the desired modifications, OK out of the Frame dialog,
choose the "New documents based on this template" button, and OK out.
If it's actually the Envelope Return style you want to modify, then you can
use Format | Paragraph to add some Space Before. You can't make it any
closer to the top without changing the envelope margins, which are set by
Word at 0.25" top and 0.5" left (you can override the left margin by giving
the Envelope Return style a negative left indent), but I doubt that your
printer can print much closer to the top than that, anyway.