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Several diffuse interstellar bands (DIBs) have profiles with resolved sub-peaks that resemble rotational bands of large molecules. Analysis of these profiles can constrain the sizes and geometries of the DIB carriers, especially if the profiles exhibit clear variations along lines of sight probing different physical conditions. Using the extensive data set from the EDIBLES survey we searched for systematic variations in the peak-to-peak separation of these sub-peaks for the $λλ$5797, 6379, and 6614 DIBs in lines of sight with a single dominant interstellar cloud. We used the spectra of twelve single-cloud sight lines to measure the peak-to-peak separation in the band profile substructures for these DIBs. We adopted the rotational contour formalism to infer the rotational constant for each DIB carrier and the rotational excitation temperature in the sight lines. We compared these to rotational constants for linear and spherical molecules to estimate the DIB carrier sizes. All three DIBs have peak separations that vary systematically between lines of sight, indicating correlated changes in the rotational excitation temperatures. We derived $B_{6614}$=$(22.2\pm8.9)\times 10^{-3}$ cm$^{-1}$, consistent with previous estimates. Assuming a similar rotational temperature for the $λ$6614 DIB carrier and assuming a linear carrier, we found B$_{5797}^{\rm linear}=(5.1\pm2.0)\times10^{-3}~{\rm cm}^{-1}$ and B$_{6379}^{\rm linear} =(2.3\pm0.9)\times10^{-3}~{\rm cm}^{-1}$. If the carriers of those DIBs however are spherical species, their rotational constants are half that value, $B_{5797}^{\rm spherical} = (2.6\pm1.0)\times10^{-3}~{\rm cm}^{-1}$ and $B_{6379}^{\rm spherical} = (1.1\pm0.4)\times10^{-3}~{\rm cm}^{-1}$. We estimate molecule sizes that range from 7--9 carbon atoms ($λ$6614 carrier, linear) to 77--114 carbon atoms ($λ$6379, spherical).