One of the possible solutions would also be to completely overhaul and just start from scratch to make a new cms specific for that however I just feel like that may take too much time.

Yeah, and then some :)
That's one of those things that will balloon way out of proportion.

Plus the learning curve of drupal is also putting me off from using it, I don't mind the learning curve as I am willing to spend plenty of time on this however an easier system would be preferred.

As a former Drupal coder, Drupal is a great platform for web development, it's well worth the time investment if you're going to be building a range of sites.  It is a different tool for a different job than Elgg though.  It's more for consumption sites - sites that are managed by a small group of content creators where the content is consumed by a large number of viewers.  Elgg is a tool for creating sites where a large number of content creators shares content either publicly or amongst each other.

Given the amount of flexibility I require in the code and cms which cms would you guys recommend and why?

What you described falls into the Elgg category.  It's likely doable with Drupal as although you said 'complex social network' you didn't really give any examples that are overly complex, but as I mentioned above Elgg is the better tool for the social aspects of what you want.

Is the learning curve of Elgg high or low, taking into consideration the project with all of the changes.

I found the learning curve of Elgg easier than Drupal, however I already had experience in Drupal first which may have helped me get started in a framework environment.  I'd guess that the learning curves are probably more or less equal.  It's like asking if the learning curve is easier with a wrench or a hammer... it depends on what you're trying to do with it that counts.