This is also on the same guidance page, section 14.14, and I think this also adds yet more weight to the arguement in your favour.....
14.14 - Children of fiancé(e) / proposed civil partner (Rules paragraph 303A)
Entry clearance with a view to settlement may be granted to a minor dependent child of a parent who has been admitted, or is seeking admission, as a fiancé(e) under paragraph 290 to 295 of the Rules provided the following additional requirements are met:
the child is under the age of 18, is unmarried and is not leading an independent life nor formed an independent family unit;
the child can and will be maintained and accommodated adequately without recourse to public funds with the parent admitted or being admitted as a fiancé(e);
there are serious and compelling family or other considerations which make the child's exclusion undesirable;
that suitable arrangements for the child's care have been made;
there is no other person outside the UK who could be reasonably expected to care for the child;
the terms of any custody order relating to the child do not prevent the child being taken to another country with a view to settlement there.
In assessing whether there are serious and compelling considerations it would normally be undesirable to exclude a child who had largely been cared for by the "fiancé(e) / proposed civil partner parent". With regard to another person being able to look after the child, this would include a close family member if there had been a genuine transfer of responsibility prior to the application. The age and health of the present carer will need to be taken into account in determining whether that person could be reasonably expected to continue caring for the child.
I have underlined the important part in this statement, the fact that NO COURT ORDER has ever been put in place!