They did it with organ transplants, and no lawsuits that I know of. The blood issue has been a thorn in the side of the WTBTS for a long time. It's the only thing that many people know about the b'Org. I think they will jump at the chance to make this a conscience issue.
I wasn't really around to know first hand but what I have gleaned on the suggests that organ transplants were a much less contentious issue. Anyone with more first hand experience please feel free to correct me, but less people were directly affected than with blood. There was not a perception in society that not accepting an organ transplant was crazy, in fact a reasonable proportion of society would likely have felt they would not have wanted someone else's organs in them.
The other factor is that the intervening years have seen a vast increase in civil litigation. Society is far more litigious, settlement figures far higher and lawyers more willing to take on claims on a no win no fee basis than it was 20, 30 let alone 40 years ago. The increase in the numbers of Witnesses with the associated increase in the numbers of lives ruined by taking a stand the blodd issue and the numbers of embittered ex-Witnesses only raises the stakes far beyond the risks the society had 40+ years ago.
Imagine a group action against the society....
It's far easier to let technology make the whole thing a conscience matter and in 10 years time it won't even be an issue.