WP uses header image's GUID as URL

[bersbers]

See summary. If I move my site (old domain becoming inaccessible), I cannot use my header images any more since
a) I am not allowed to change GUIDs.
b) GUIDs are used as URLs for header images:

http://core.trac.wordpress.org/browser/trunk/wp-includes/theme.php

1008        foreach ( (array) $headers as $header ) {
1009	                $url = esc_url_raw( $header->guid );

I am not sure, but it seems that event newly uploaded files receive a GUID that contains the OLD domain. This means I cannot even re-upload header images, I cannot use any header image after moving a WordPress site. Can this be true?
(Probably not true generally. It does however seem true when I simply re-select the old header images from the media library. So I really need to re-upload ALL header images after moving the site?)

Use wp_get_attachment_image_src() for URL

Not sure about the size argument. Is there a registered size for header images I missed?