Mr. Kendrick:
Since you now claim that the address is the important element here, I have a suggestion. Do what I have done. Write a letter to Buckingham Palace and use the title Czarevitch Alexei Nicholaevitch as the name on the return address. See if you get a response. My own theory is that some Bert 'n Fred in the royal mailroom will look at each other and shrug, and send it out --- on the theory that they have another live one on their hands. Olga Alexandrovna used to say that she was constantly being attacked by Anastasias in public places, and this strikes me as the same kind of thing.
All kidding aside, this isn't history. But it really isn't journalism, either. If it were, would you not have verified this sort of thing with Buckingham Palace? In terms of your involvement with this case as a journalist, do you have an editor?
As for whether Alexei had hemophilia or not, I suggest that we take the diagnosis offered at the time to his parents at face value, since all of his symptoms seem to jibe with it. Alexei's symptoms, not Tammets. Your arguments go in reverse order. Tammet didn't have hemophilia, therefore Alexei didn't. Nuh-uh. Moreover, the diagnosis of hemophilia was consistent across Victoria's descendants, making it virtually certain that Alexei had it as well. He was being treated for it in 1912, not 1812, and the disease was well documented by then.
Did Tammet's purported family contain other blood diseases? Did you investigate his background to discover this? Did Mr. Tammet offer a reason why he broke 54 years of being in some kind of Romanov Witness Protection Program just to send Anne and Mark a telegram? Was he fixated upon royal weddings? Was he fixated upon Anne? (I know, but weirder things have happened --- she has a certain charm, swatting away attempted kidnapers and such).
It's a tease.