  We analyze recent $K^+$ meson photoproduction data from the CLAS
collaboration for the reactions $\gamma p\rightarrow K^+\Lambda$ and $\gamma
p\rightarrow K^+\Sigma_0$, fitting measured forward-angle differential cross
sections to the form $Ae^{Bt}$. We develop a quantitative scheme for
determining the kinematic region where the fit is to be done, and, from the
extracted $t$-slope $B$, determine whether single-Reggeon exchange can explain
the production mechanism. We find that, in the region $5 < s < 8.1$ GeV$^2$,
production of the $K^+\Lambda$ channel can be explained by single $K^+$ Reggeon
exchange, but the $K^+\Sigma_0$ production channel cannot. We verify these
conclusions by fitting the data to a differential cross section produced by the
interfering sum of two exponential amplitudes.
