I don't know much about in-year transfers, so may be completely wrong, but I thought if there was a place and you applied for a transfer it could be almost immediate. I know of 2 friends whose children started at one school and transfered to the grammar within 2 weeks.
Three years ago, DD sat a test for in-year transfer (year 7) at the end of June, we were offered a place on Tuesday July 9th and she started at her new school on Monday 15th.
The school normally fills its places and at the time didn't invite girls (anyone on the CI list, including those who had failed the 11+, like DD) to test until late in the first term at the earliest if a girl left. However, the year before DD's started with places vacant and girls were tested quite early in the year as there was no waiting list (or possibly no girls whose names had been left on the waiting list who actually wanted to move schools by then). No school wants to have holes in its funding, of course, which is probably why Wirral is doing what it is doing. I guess it depends how much a girl wants to go there - UnsureMum, if your DD had passed originally and was currently on the waiting list, would you take a place if it came up at that point in the summer holidays? If, on reflection, you probably wouldn't, then the added stress and uncertainty of sitting another exam may not be worth it. But if you would, then this is the only way of potentially putting yourselves in that position.
One thing that I did, when accepting the invitation for our DD to sit the in-year test, was to ask how many places were on offer (3) and how many girls had been invited to test (25), which gave us an idea of the level of competition. Fortunately we had just had parents' evening, so we knew that she was working at a level which showed that she had a reasonable chance of at least meeting the required standard.
Good luck with your decision-making