Oh god I feel your pain OP; this happened to me too.
Changes made:
MOST IMPORTANT OF ALL:
Visiting DC at 5, then 10, then 20, then 40, then 80 mins after put down. Pat them and just say “sleepybyes” then leave the room.
It makes you feel in control and the child feels secure, both of you start “knowing the score”. Still doesn’t take away how upsetting the crying is though 
SECONDLY: persist with putting DC in cot at lunchtime, again with the 5/10/20 mins thing. We give up if our DD isn’t asleep by 40mins after put down.
THIRDLY: it might possibly be time for a big bed but I’d certainly advise moving away from grobags and onto covers (or not in this heat!). DD is tall and was out of grobags at 22mo.
Lunchtime naps are hit and miss in this house. We watch in the night garden at 6, then it’s wash face, teeth, and into bed by 6:45, cuddles and kisses then away.
Good luck. I completely get your CIO reasoning, forget the guilt trippers on this thread.