Well I imagine that by the time you read this, you would have already discovered the answer, but for what it's worth:
100g of sugar is A LOT. I use that much to carbonate around 12-15L batches of beer. In the future, carbonation calculators are your friends.
Yes, coke bottles will deform. But they WILL explode. Think about it this way: The coca cola company engineered those to use as little plastic as they need to hold the prusser of carbonated coca cola, nothing more.
My recommendation is to VERY VERY VERY CAREFULLY, try to relieve the pressure. The reason is that cold crashing does not stop fermentation PERMANENTLY, only as long as the bottle is cold. Better to let the yeast get all the way through, and relieve the pressure occasionally until you get the carbonation you want. That said, I wouldn't bother with the sieve. When the yeast is done, it will sink.