I know this hotel very well and in my case if I wanted the Royal Suite, I would simply ask them what room I needed to book to secure the Royal Suite. Or effectively how much do I have to pay.
So my advice to someone who is not well known by the hotel would be to have a pleasant discussion with the reservation manager and ask about general RA upgrades, and then move up from there to see what you'd have to pay to get the suite you want.
And again, it depends on availability or even projected availability. In July and August for instance, there exists a group of people who often book out the top suites at this and a few other of the better Euro IC's.