Domain mapping - forced https in backend and customizer doesn't load

Here's an interesting one for you. I have domain mapping installed on my network, I have around 90 sites, around 80 have mapped in domains, the rest are the original subdomain urls. I have installed an SSL certificate and forced https in the backend. I have set domain mapping so that admin pages and login pages show the original subdomain rather than the mapped domain.

There is one major issue with this setup, when I open the customizer, I get the following error in the console:
Mixed Content: The page at 'https://website1.skizzar.com/dashboard/customize.php?return=%2Fdashboard%2F' was loaded over HTTPS, but requested an insecure resource 'http://website1.com/?customize_changeset_uuid=19eb48b5-7b7f-4042-9ec1-079406b0f1a5&customize_theme=pastorious&customize_messenger_channel=preview-0'. This request has been blocked; the content must be served over HTTPS.

...and as a result the preview of the customizer doesn't load. If, however, I make a change in the customizer, then the preview will load.

Here is a screencast video showing my issue:
https://drive.google.com/file/d/0Bz7QPMwRx89ZcmFtZkJxSkFOYU0/view

Can you think of any way to resolve this issue?