The performance of advanced fluid neutral models for the simulation of deuterium atoms in the plasma edge of magnetically confined fusion devices is tested for the first time on cases that include drifts and currents in the plasma model, on a simplified Alcator C-mod case. The unadapted advanced fluid neutral model already gives quantitative agreement, with 5–30% fluid-kinetic discrepancy in the broad vicinity of the strikepoint. A new advective perpendicular transport term is proposed, which further reduces the fluid-kinetic discrepancies for cases with drifts. It is also shown that the ion-neutral current can be calculated consistently for fluid or kinetic neutrals, at least when only atoms are considered. However, its effect on the solution is very small for the studied case.