I think your suggestion to start contact sessions with the grandparents is the way to go. You can put this in your position statement but discuss this with the duty Cafcass adviser before the hearing, as the Section 7 recommendation seems to go against contact (see below).
You should refute the lack of consistency allegation - I think you said there were many other reasons why there were barriers - which weren't from you. I'm not sure I understand the not being a power imbalance reasoning, but the fact that they don't recommend Fact-Finding is a very good thing. Practice Direction 12J says that in Domestic Abuse cases, if a Fact-Finding hearing is necessary to determine if the allegations are true or not, in case they are, it's safer for the child not to have contact with the alleged abuser until the FF hearing has taken place. Because your letter does not recommend a FF hearing, it means that Cafcass probably have doubts about the mother's stories about abuse. If she was more convincing or there was Police or Child Services evidence to support her claims, then they would say a FF hearing is necessary. That is a good step forward that they don't.
[In my case, Cafcass did recommend fact-finding, but because I was able to show the safeguarding letter was wrong, the judge disagreed with fact finding saying the wellbeing of the child is more important.]
I'm not sure about the Family Solutions involvement letter - what did that mean? What was the Local Borough assessment?
The letter implies that a Section 7 report should be done to figure out the next steps, but also implies there shouldn't be contact until this is complete. There's nothing to stop you from saying that to re-establish contact between the father and the child is the most important thing for the child's welfare, and if a Section 7 report is necessary, it could be done concurrently.