If I understand you correctly your problem is basically that the background image doesn't align with the plan you already have.
As far as I know you can't manipulate the background image once it is imported so one solution could be to rotate the image in a program like GIMP and save it that way. Then import the rotated image in Sweet Home 3D.

There is another solution that might be easier:
First install the plug-in manager: https://sourceforge.net/p/sweethome3d/plug-ins/44/
Using the plug-in manager install the Advanced Edit plug-in. (This is one of the essential plug-ins that you will use a lot.)
Open your project. Make sure everything you want to reposition is visible on all levels.
Select from the Edit menu "Select all at all levels".
You can now use the functions Rotate and Move to position your plan to fit exactly over the background image.