Sandy was moving fast when it hit the coast. It was a major rainmaker just due to shear size though. Even moving fast a storm system that is nine hundred miles across has a significant interval between impact and eye landfall.
I'm not sure about the aggregate numbers, but where I lived at the time, Sandy's rain did not cause much flooding. Floyd, which came through in '99 IIRC and was only a tropical storm by the time it reached NJ, caused much more serious flooding. We didn't get significant power outages but for example Rutgers university closed for two days because of flooding on roads around the state. I remember how well how high the Raritan River was, and the two parks in my hometown along the river bank were completely flooded - you could only see the roofs of the playground structures above the water - and it took a few weeks for the water to go back down. Sandy didn't even come close to that - the Raritan overflowed its banks but it just made the parks swampy and puddly, rather than putting them under 10+ feet of water.
Main problem with Sandy was the coastal flooding from the storm surge, and the fact that the winds over such a large area had taken out power for a huge number of people. My parents' block had a pole go down so their house, fourth from the corner, and the other three houses were without power for eleven days. Thanks to the snow that came through shortly after Sandy they had to stay with friends who got power back sooner, and my dad and brothers eventually drove up to Saratoga Springs NY, where my mom was already staying with
her mom when the storm hit (purely by coincidence). They stayed up there for more than a week until the house had power again because it was too cold to stay in the house without power.
Fortunately, the house I was living in for school was half a block away from the hospital, so it had its own power. WE had a full week of cancelled classes because of power outages all over the state, and there was something of a carnival atmosphere in town. Liquor stores weren't carding anyone because their computers were all down. Glorious week. Ruined my grades that semester though.
As long as the eye is over water it will be hoovering in makeup water to sustain the rainfall longer. If the track moves just a short distance to the west and puts the eye over land before it stalls there will be a lot less accumulated rainfall.
Yeah, this is true. IIRC most of the inflow happens in the area immediately surrounding the eye.