Have you asked your supply agency, or one of your supply schools, for help? I know the agency wouldn’t want to lose you to full-time work, but it is worth a try. If you do reach the end of your time limit it is possible to ask for an extension of your supply time of up to 12 months in the local authority where you wish to do supply work. I think you have good grounds for an extension as you have clearly been trying for an induction post.
Remember also that any part time work or full time work that lasts for at least a term regularly teaching the same class or classes must count as induction regardless of whether this job is provided by a supply agency or direct with a school or local authority.