I think it's very hard to make anything help. Here's a shortlist of things that should be fixed to avoid it horribly hurting innocent people, but I doubt it's enough - there seems likely to be more things in there. The original purpose of the law seems to be "Give the 'intellectual property' industries a blunt instrument to attack perceived violators", so making it less blunt probably violate the original purpose anyway.
Stop removing DNS entries; that's attempting to censor things that aren't in the US for non-US citizens.
Require a full court proceeding to stop advertisements and payment processing in the US - ie, no "court order", it has to be a full lawsuit with the ability to defend.
Require the removal of access to only affect a specific, listed set of companies.
Require the company requesting the blocking to pay reasonable costs of blocking.
Remove the making of copyright infringement into a felony; each of these things can easily happen by mistake.
Stop removing DNS entries; that's attempting to censor things that aren't in the US for non-US citizens.
Require a full court proceeding to stop advertisements and payment processing in the US - ie, no "court order", it has to be a full lawsuit with the ability to defend.
Require the removal of access to only affect a specific, listed set of companies.
Require the company requesting the blocking to pay reasonable costs of blocking.
Remove the making of copyright infringement into a felony; each of these things can easily happen by mistake.