I'm the third person to jump in this, i'll be available tonight until about 6pm to answer your query, I have conferred with both Carly & Eddy on this.
You're right, you don't want any submission to suggest that the director has been an employee since February, as the director is the director.
Have you spoken to HMRC yet regarding this? I'd be curious as to their opinion. I don't think HMRC are completely neccesary, but they can sometimes offer guidance.
I am of the opinion to agree with my colleague @EdwardR, You would put the start date and director date to be the same. Personally, I would put the start date as the date the director became director, and the appointment date to be the same date.
Think of it this way, you could have a business active, where you are the director and only member of that business for a year, even longer sometimes before pulling a wage for yourself out, that doesn't change the date you started with the company, nor does it change the date you became director. The information our system is looking for is the real life information, so in the case of your example, i'd pick Feb 1 2018 for both start & appt dates.