I dont think you can really stuff anything soft into holes in ships that deep or large? Are the forces involved not very large....... we are talking maybe putting something large like a canvas hatch cover on the outside to get sucked in but pushing against the water would be next to impossible apart from maybe with hitting in wood in small holes but even then low down deep in the hull the flow in would be strong? She had a draught of 34 ft 7 in (10.5 m) so damage low down is going to be maybe 8m underwater?
I assume the crew would know about driving wooden wedges into gaps in the plating to slow influx of water. As you mention, the pressure is strong, so it must first be reduced, by doing something like putting a canvas hatch cover over the gap from the outside. Else, no one will be able to. The water is cold, so men have to be rotated out of damage control, and into the warm boiler rooms to keep them alive.
So, in an ideal situation: After striking the berg, the ship is immediately stopped while damage is assessed. Passengers are roused, and instructed to be ready to abandon ship. Assessment shows that they should attempt damage control on compartment 5. They lower a canvas cover over the area, slowing water inflow enough that the pumps can keep up. When the compartment is pumped clear, more permanent control is affected. Wedges, bracing bulkheads, etc. Maybe she still sinks, but it takes longer. If she can stay afloat long enough for other ships to arrive, I imagine that they have portable pumps that can be set up to help, as well as talking passengers off. Presuming she isn't too far gone already. With compartment 5 controlled, they start work on the next forward, lowering another hatch cover, allowing the pumps to clear it and do the same.
Saving the ship is ideal. As was, they did nothing but pump, no attempt to slow inflow of water. Doing something might help, and cannot hurt. At the least, time is bought. At the most, the ship is bought.