since the Soviet Union has opened up its archives?

aahahhahaa

That's not happening any time soon. At least, the stuff pertaining to secret services and so on.

A more accessible source is the (fairly recent) 'MI6: The History of the Secret Intelligence Service 1909-1949', by Keith Jeffery (2010), an authorised history of the service compiled with surviving source material (much sensitive material was disposed of which made Jeffery's job harder). Reilly (born Shlomo Rosenblum) is treated on fairly extensively in this source; his exact date of death is listed as 5 November 1925, having been duped by the OGPU (Bolshevik secret police) in a sting operation called 'the Trust', a fake Russian monarchist group.

Source: aforementioned book pp183-184, see also pp134-6, p138, pp174-184, p215.

His citations concerning the death of 'Reilly' are Spence, Richard B. Boris Savinkov: Renegade on the Left, Columbia University Press, 1991 and Andrew Cook, Ace of Spies: The True Story of Sidney Reilly, 2004, Tempus Publishing.