So to report back, I did my plan as stated above but the lounge was packed when I first tried to go in around 14:30 but cleared out enough in about 40 minutes for me to get in. I had a few hours to kill so not a huge deal.
I didn't realize that a PP entry grants you a choice of an a la carte menu in the No 1 Lounge. It looked pretty good from what I saw around but having just eaten, I wasn't too interested.
If I had to do it again, I'd reverse the order and try and get into No 1 first and just eat there and then use Granary Store as my backup.
That said, the Granary Store burger was pretty good and definitely a good deal to end up with a 50p bill for a burger and water.