My problem is that the book (Essential University Physics, Wolfson) has the answer as -4.17 kW, but that would imply that heat is being transferred from the ground to the house, which it clearly cannot be from the temperature of the house being larger than the ground's temperature.

I usually have problems with the sign of this value of H, how do I know what direction they are asking for by "through" an object - it could be either. Would either value be acceptable in an exam?

First of all you have given K to be 1.0W/mK. which means 1000W/K to be used in the equation . This gives the answer to the equation to be 4.17kW.
As to which direction, heat flows from hot to cold.
Sometimes worrying about the signs that crop up in equations can be confusing..... they are never 'wrong' but don't forget common sense.