Part of the problem, from what I understand, is that not all African-Americans even recognize that as the day to celebrate - I know some who view January 1 as the proper date because that's when the Emancipation Proclamation went into effect. There's also the date for the passing of the 13rth Amendment, and for it becoming official US law with the last state necessary ratifying it. (With the others doing so later, of course.)
If you could get 2 of the 3 to agree, or at least be very close (so it becomes like Presidents' Day, a combination of Washington and Lincoln birthdays), that would make things a lot easier. Let's say an earlier passage of the 113th Amendment in 1864, either around June 19th or early enough so that it is ratified in enough states to become effective around June 19th, 1865. That might make it much more likely - as noted, it could be off by a few days.
How did Lyndon Johnson view it? He was from Texas, so if he'd pushed more for it on the 100th anniversary that might have helped, but that might have been harder at that time with Civil Rights just then being passed.
Alternatively, have
Claude Black arise as the most renowned Civil Rihts leader in U.S. history, and he might suggest it - especially since he lived long enough that a holiday honoring him might be prposed and he'd be around to turn it down and have the tradition of Juneteenth to point to instead, being from Texas. Interestingly, I have heard some very conservative white Americans say they would rather not celebrate Martin Luther King because of his association with Communists, but *would* be okay celebrating Juneteenth because it was the end of the Civil War and could be for black people as the end of slavery. I wonder if it's possible for Juneteenth to come about as a holiday instead of Martin Luther King Day. One thing that would help would be a TExan who would push for it instead to be a co-leader or especially seen as the main leader instead of Dr. King.
Now, how to get Claude Black to become that? Could he trvel to Alabama a few time instead, then become involved in a number of thigns, perhaps making the most famous speech of the March on Washington?