However summer born children, which both of yours are, now have the option of starting reception the September after their fifth birthday
I'm afraid that is not true.
The OP can apply for her child to start Reception a year late but the decision is for the admission authority (the school or the local authority depending on the type of school). The admission authority must consider each case individually rather than implement a blanket policy but they do not have to comply with the OP's wishes. Some LAs will allow delayed entry on request, others will only allow it where there is significant evidence that the child has developmental delay.
Even where the admission authority allows the child to enter Reception a year late, it is important to check what will happen on transfer to secondary school. Some secondary schools insist on returning children to their "correct" year group, resulting in them missing either Y6 or Y7 completely.
The OP can defer entry until Easter. That is her choice. Beyond that it is up to the admission authority.
The research backs this up
The research certainly suggests that summer born children perform worse at school than children born at other times of year. However, research on the effect of delaying entry for a year is mixed.
The 6 year old would then probably go to the top of the list for a place in year 2 or year 3 as a sibling
Possibly but many primary schools only prioritise if the child has an older sibling at the school.
Then submit online
The OP cannot follow the last paragraph of your advice at all. She is in Scotland. Unless she moves to England in the next 5 days (which she is clearly not planning) she cannot apply for a school place in England. She has to apply to the local authority where she lives. Local authorities in Scotland do not handle applications for places at schools in England.