Insulation is intended to create a clear boundary between indoors and outdoors, thermodynamically speaking. In this case, that thermal boundary was pretty porous because of all the pipes, ducts, and wires penetrating the boundary. One way to deal with lots of penetrations in the attic floor is to put the thermal boundary at the roof—in other words, to insulate the rafters rather than the attic floor.
But this house has a slate roof. Slate is a great roofing material, but slate roofs frequently leak. Much of the time it doesn't really matter: the old roof sheathing boards that the slates are nailed to absorb the water and when the sun comes out the board sheathing dries out, and no one's the wiser. You only have a problem if the roof assembly takes on more water than it can readily absorb, which was the case with this roof.
To insulate other slate roofs, we've installed vent channels between the rafters that also act as drain chutes to allow water to escape through the soffit vents if (when) the roof leaks. We've then sprayed foam insulation against those vent channels. This is a pretty safe way to insulate under a slate roof. At this house, though, the rafters run in all directions--not just from ridge to eave. So installing the combination of drain/vent channels was not an option.
Instead, we decided to maintain the thermal boundary at the attic floor, sealing up as many air leaks as we could and installing a lot of insulation on top. We used our blower door for quality control during air sealing and were able to reduce the overall air leakage of the entire house by half - just by doing a good job in the attic. After that, we blew in 18" of cellulose, for a total R-value of over 60, which is almost twice what code requires (cellulose is a cheap way to super-insulate a roof, so there's no reason not to use a lot of it).
The day after we finished, we got a good test: over 24" of heavy, wet snow. We went by the house to check things out and were extremely psyched to see that there were absolutely no ice dams or even any icicles. Our efforts to prevent heat loss from the house to the attic were an unequivocal success. Not only did we solve the ice dam and roof leak problem, the house is more comfortable, quieter, and cheaper to heat and cool.