If jack is OT then he tends to need a nap around 20-30 minutes earlier than usual, so working back from that, I'd have thought a nap at 12.15 when OT means a normal nap time of 12.35 - 12.45 should be about right? A few months ago jack would nap at 12.15 when OT but 12.45 normally, so you could try putting her down half an hour later after a catch up day?
Sorry, just seem your edit. How did it go?