It all fine as you have stated.
You can train and sit your skills test on a lapsed class 1 medical to class 2. In fact you could even do it all with no medical at all as there is no point which you will have to fly solo.
I did my cpl/ir and FIC all on a lapsed class 1 and only got a class 1 again the day i sent all the paper work off.
mj