When is this big birthday? With the busy period until about 15 July in London, if this is for a short term window, changing to another property might be overly costly. I too would try and talk you out of the Savoy, but with keeping the above in mind

While I like the team at the Milestone, The FS location is tops. If you do keep the Savoy then the FS location could be major plus for those last few days. I suggest you take a look at FS Preferred Partner which is discussed extensively here to combine the 4th night promo with some perks.