There's a trick using the Custom Script Assistant that should make life easier. Rather than putting the text behind the image, try this:

1) Select the image.
2) Go to the "Tools" menu and select "Custom Script Assistant".
3) Make sure the "Object Events" button is selected.
4) Enter the following code in the "Contents" box:

alt="whatever text you want"

5) Click OK.

When you preview the site, you should see the text entered in step 4 as the ALT text for the image.