The Republican party is to blame for not using the Civil Rights and Voting act to it's benefit. As you said electing Barry Goldwater sent the wrong message off the bat
Very true, but it still brought zero benefit to the GOP. LBJ got all the credit for it.
then the Southern strategy didn't help.
Which was in response to the 1964 election. Nixon concluded that the GOP didn't need the black vote to win and he's right. The GOP held an electoral advantage for the White House for decades in the post-Nixon era thanks to Nixon's Southern Strategy and Reagan turning the United States from a center-left nation to a center-right nation.
It took major demographic shifts, the increasing prominence of women and Hispanic voters to erode that advantage away.
Look at it this way, if the Republicans can pass a votings right act it gives them some credibility that they doing stuff for the black and minority community. Positive benefits of that are
1. it could slightly eat into the minority demographics
2. it will make it harder to attack the GOP in turn out the vote campaigns(which indirectly can cut down the amount of voters who feel inclined to go out and vote)
3. People who aren't minorities but are indirectly turned off by the Republican party's stance on minority issues, might view them more positively(ie the suburban housewife vote)
I don't see them doing it because the base will go batpoop crazy, but if they somehow could pass it with a huge majority of support that could potentially be a game changer in 2016
I think you're being rather generous into how much black support the GOP can eat away from the Democrats.
Also, eating away at Democratic advantages with blacks will bring almost no benefit to the GOP. The majority of blacks either live in the Republican dominated South or in Democratic states where there are major metropolitan areas like New York City, Detroit, Philadelphia, Chicago, etc. The only states that I think would shift more Republican with your presumptions would be Virginia, North Carolina, and Florida. Not a lot of benefit there, especially when you consider the fact that Republicans already hold a lot of significant advantages in those states.
But reaching out to women and Hispanic voters would do more to shift Virginia, North Carolina, and Florida to the Republican column along with shifting a lot of other states like Colorado, Nevada, and Ohio.