From my experience:
I applied for WP when I received the nomination letter + support letter from Alberta during that time (My PGWP still valid and it would be expired within 2 months). It takes time for you and your employer to submit the info. Your employer need to fill in the forms and pay.
I don’t think we can apply for open WP. If you use the support letter to apply for WP, it will be a close WP, which means you can only allow to work for the same employer.
I will suggest you to apply for WP ASAP. Once they refused the BOWP, then no working is allowed until obtain a valid permit. At this point,
I don’t know if we can still use the support letter to apply for WP because technically we are not working under the same employer so we may need LIMA.