I think your best bet is to keep chipping away, slowly and carefully. I had a clump of blue rush that was getting out of hand and I spent the better part of a day in the pond (this was July or August) with a pruner and a hand trowel, cutting and pulling and chopping. Like you I was very afraid of damaging the liner, but slow and steady work allowed me to see where the liner actually was and work without damaging it. It took me hours of slow tedious pullng and yanking and cutting but eventually I got it all out. I really doubt it's pierced the liner - these types of plants just tend to find the path of least resistance. Mine had gone over the liner into the surrounding landscape, but it made no attempt to go through the liner.
The next spring I discovered it had re-seeded itself across the pond. Haha.
Here's my other tip - we had some pond work done last season and had a few low edges addressed by the pros. Those hardy young men could yank those pond plants out with a few good pulls. Get yourself one of those and save yourself a boatload of time! Just make sure they are experienced with working in a liner pond.
The moral of the story is: keep your pond plants in check at all times. Never ever turn your back on them. They will defeat you.