When a planet is only observed to transit once, direct measurement of its period is impossible. It is possible, however, to constrain the periods of single transiters, and this is desirable as they are likely to represent the cold and far extremes of the planet population observed by any particular survey. Improving the accuracy with which the period of single transiters can be constrained is therefore critical to enhance the long-period planet yield of surveys. Here, we combine Gaia parallaxes with stellar models and broad-band photometry to estimate the stellar densities of K2 planet host stars, then use that stellar density information to model individual planet transits and infer the posterior period distribution. We show that the densities we infer are reliable by comparing with densities derived through asteroseismology, and apply our method to 27 validation planets of known (directly measured) period, treating each transit as if it were the only one, as well as to 12 true single transiters. When we treat eccentricity as a free parameter, we achieve a fractional period uncertainty over the true single transits of 94-58+87 per cent, and when we fix e=0, we achieve fractional period uncertainty 15-6+30 per cent, a roughly threefold improvement over typical period uncertainties of previous studies.