Even if we halve the patent protection period, that is still ten years during which a patent troll can scoop up a BS patent and then simply send threat letters and rake in money, while chilling any actual advancement.

Currently, there's an incentive to disallow progress. If someone does not want to make use of their own patent, they are currently incentivized to sit on it and keep the ability to create that thing out of the hands of anyone else, "just in case". If we shorten the period as you suggest, to half (for example), then that freezes that progress for a decade.

If an incentive is created to put inventions into the public domain if one is not using them, then that is better for everyone.

And by doubling the fee each year, it becomes financially infeasible for even large companies to keep things out of the public domain forever. A fee of $500 that doubles annually would, at the 20 year mark that is the current patent lifespan, cost a half a billion dollars to renew for that year.