G'day,
I'm a talented Linux DevOps engineer with over a decade's experience in the field. I've worked with various APIs to administer cloud services and VPS's in the past. I have complete confidence in my ability to resolve your issue successfully and quickly.
From the description of your problem it sounds like what you need to do is create the new droplet, without immediately adding it to the load-balancer, and then after the droplet is setup and ready to go you need a separate API call to add it to the load-balancer.
I can think of at least two ways to do this, and I'd be happy to discuss with you what would work best with your environment.
(Note: I actually expect this to take a lot less than 6 days, but I'm allowing some flex-time in the deadline for the upcoming Easter long-weekend)