Joseph – Re starting SE late: If you know for sure you can reach Elokai Netzor before the chazzan reaches Kedusha, then you can daven SE now even though you are starting late.
Otherwise, daven with the chazzan during chazaras hashatz so that you get the zechus of answering Kedusha.
In all cases [with few exceptions that we will not get into now], SE must be started immediately after uttering the words ‘Gaal yisrael.’ You cannot pause silently or say something else in between. This applies on a weekday for sure, and possibly also on Shabbos.