Can a future choice affect a past measurement's outcome?

An EPR experiment is studied where each particle undergoes a few weak measurements along some pre-set spin orientations, whose outcomes are individually recorded. Then the particle undergoes a strong measurement along a spin orientation freely chosen at the last moment. Bell-inequality violation is expected between the two final strong measurements within each EPR pair. At the same time, agreement is expected between these measurements and the earlier weak ones within the pair. A contradiction thereby ensues: i) Bell's theorem forbids spin values to exist prior to the choice of the spin-orientation to be measured; ii) A weak measurement cannot determine the outcome of a successive strong one; and iii) Indeed no disentanglement is inflicted by the weak measurements; yet iv) The weak measurements' outcomes agree with those of the strong ones. The most reasonable resolution seems to be that of the Two-State-Vector Formalism, namely, that the experimenter's choice has been encrypted within the weak measurement's outcomes, even before the experimenter themselves knows what their choice will be. Causal loops are avoided by this anticipation remaining encrypted until the final outcomes enable to decipher it.