This scenario is probably the second worst nightmare of most sailors (I would think fire is the worst). I'm sure you'll get lots of different suggestions, but I would be thinking about the possibilities (thinking very fast!):
1) Ensure my bilge pump is pumping (though most can't keep up with a decent sized hole, but better than nothing)
2) Try to determine location of water coming in, including checking seacocks if time permits, depending on how much water is coming in; this is harder if you have an interior hull liner as you noted, but if necessary, use tools to break it apart to get at the holed area.
3) If possible, try to stuff cushions, blankets, sleeping bag, etc. into the hole to stem the flow, perhaps reinforcing it with a wooden board (locker top) wedged against it
4) I would try to run my smallest sail under the boat in the area of the hole (ie. probably under the bow in your scenario), tied off to either side to stem the flow into the boat
5) If the water is still rising, I might undo the engine water intake from the seacock, start the engine and have the engine suck water from in the boat
6) Depending on the situation, I would at some point have radioed for help; if I wasn't at immediate risk of sinking, I would likely delay this a bit to try other options first, so I would know what kind of help I might need.
7) I would ensure that my safety gear is at hand--life raft, life jacket, EPIRB, handheld radio
8) Time permitting, I would have wallet and valuable papers at the ready to take with me, if I have to leave the boat
9) If I have the situation under control, I would then think about more permanent fix--epoxy patch, etc.
These are just my initial thoughts, so I'll be interested in what others would do. Good question.