As I see it, there's two issues here:
1. whitehouse.gov isn't 508 compliant / usable by blind people. A technical issue that must be fixed. I believe there are captcha implementations that are blind accessible, surely it'd be an afternoon's work to swap their current implementation out for a better one.
2. Because of 1, it's not getting the signatures it should.
I'm sure they're aware of #1 - and promoting this piece and others like it will help raise awareness of the issue and prompt them to action.
As for #2, solving that is simple: you've already signed the partition, right?
Maybe it should be written into law that contracts based on patents must, through some mechanism, grant the people involved the right to sue for some compensation over invalidated patents. - of course the trolls will inevitably find a way around this, but it's a start.
So this way if Company A pays up, then Company B fights and wins and the patents are declared invalid, Company A has grounds to sue the troll for compensation. Of course they'll never get back the full amount they paid up as they'll have to shell out some cash for lawyers and stuff, but in the end it'll be another cost for the troll.