Update! I heard back from the Director of Sales.
Obviously they won't guarantee anything, and they've reminded me that they're refurbishing currently so some rooms are out of action, and also that they do have many large corporate clients. However - they have said they will try their best to upgrade our Plat and Gold members if they can, AND - the important part - they've manually upgraded all of my upcoming stays to exec rooms - so I'm happy!
I consider that a reasonable result - I wasn't expecting to suddenly be treated like royalty, but to have their word that they'll try and to have all my upcoming stays upgraded was a pretty reasonable deal.
I guess I just got lucky in the other property where I've been upgraded on every stay (including 3-4 week stays) over the past year or two I've been staying there - this is probably more the norm.
Thanks all for your help and advice - very much appreciated and I think that was the right way to approach it. Cheers.