Relating V1 with Vmcg in this discussion could be misleading - a decision speed with control characteristics required for continuing the takeoff, but not directly the distance required to stop.
Reduced thrust may not be authorised by your regulator. 'The AFM states, as a limitation, that take-offs utilising reduced take-off thrust settings – Are not authorised on runways contaminated with standing water, snow, slush, or ice, … ' (CS 25 ref)
Risk - uncertainty - CS 25 AMC 1591
8.1.1 Operation on runways contaminated with water, slush, snow, ice or other contaminants implies uncertainties with regard to runway friction and contaminant drag and therefore to the achievable performance and control of the aeroplane during take-off, since the actual conditions may not completely match the assumptions on which the performance information is based. Where possible, every effort should be made to ensure that the runway surface is cleared of any significant contamination.
8.1.3 The provision of performance information for contaminated runways should not be taken as implying that ground handling characteristics on these surfaces will be as good as can be achieved on dry or wet runways, in particular following engine failure, in crosswinds or when using reverse thrust.
"Risk is the amount of uncertainty which operators have to manage".
Do not ask "how can this be done", but "should I be doing it".
How - is theory; its the doing which involves risk.