The battery is quite healthy. Its a 1 year old group 24 deep cycle. It could probably crank the engine for a good half hour.
Honda's IMA only stops the engine under X speed (I'm not sure what it is, or if it differs from car to car). Mine will stop the engine any time you shift to neutral. Therefore, if you want the engine to keep running, but you want to coast with the engine on, you'd need to keep the car in gear, but push the clutch in. However, you are correct about the neutral engine stop delay. I currently have it set to two seconds. I figure thats ample time to shift and find the next gear. It may take some tweaking, but thats the current action. I'll also include a switch that shuts the unit off and reverts to normal operation since I would probably not use it a ton while driving unless it works really slick.