Good luck with the argument about double stay credit for paying for two rooms in two places. As you noted, it has been tried, and discussed here, once or twice a year since Noah parked the Ark. Hyatt IT has a good record of picking that up and not granting double stay credit. Their philosophy is you can only sleep in one place in a night. So one stay credit for you. If you figure out a dependable work around to get two credits we're all ears. To them it is like phantom stays. A logical case can be made, but either you are in the bed are you are not.
Since you are in Britain or going there soon: What is the weather like in London and the Scottish Highlands in October, and in April? Trying to balance a trip there next year with some expiring pre-paid nights in Hawaii.