I entered the results in America Votes 7 into a spreadsheet. And on comparing them to the 1964 Presidential results from Mississippi, I made these breakdowns of how counties voted in the 1963 Gubernatorial race and the 1964 Presidential race.
Counties which went for Phillips went 54/46 for him and 81/19 for Goldwater.
Counties which went for Johnson but gave him less than 60% went 55/45 for Johnson and 85/15 for Goldwater
Counties which went for Johnson and gave him more than 60% went 69/31 for Johnson and 90/10 for Goldwater
The vote distribution in those counties-
Phillips: 15% of the vote in 1963, 16% in 1964
Johnson 50-59: 28% in 1963, 29% in 1964
Johnson 60+: 57% in 1963, 55% in 1964
Here's the manually-drawn county map for the 1963 election (with the county totals not entered here since the only source is America Votes):
62/38 Johnson, but it was the first time a Republican had run for Governor in around 80 years.
Info on Phillips/Johnson:
http://www.cresswellslist.com/ballots2/phillips.htm