it appears that anyone who says fixed "helps" them on dead spot hasn't learned to pedal efficiently in circles. i didn't feel any help on fixed, unless i deliberately tried to pedal in squares, i.e. mash the pedals. next time, when you can feel that fixed bike is helping you, try to pedal so that it doesn't.
as for keeping the momentum when the road goes up - it's clearly felt on ss too and is a bit of a bummer when you are in the middle of the group. you want to accelerate while the road is just getting steeper to carry the momentum as far as possible, otherwise you know you'll suffer more!
regarding efficiency - both fixed and ss drivetrains (and bikes) save around 8w compared to geared, so in the right range they are a bit quicker - that's why i chose a ss bike for one of my challenges. headwind all day long has thwarted my attempt, but still managed 613km in 24hr on 58 x 19 (81"), and it was a good preparation for pbp (i had a geared racing bike in a support vehicle, as a backup).