I actually think that Reagan winning the Republican nomination, under the right circumstances, could help facilitate Wallace’s victory during the Democratic primary season rather than hindering it. It sounds counterintuitive, but hear me out. You are right that the two candidates often drew support from the same set of voters, especially in the South, but that does not tell the whole story.
See, during the early stretch of primaries, Reagan was sort of floundering. Ford had won New Hampshire, which was arguably a bit of an upset, and then crushed his opponent in several more contests. The Gipper’s campaign was only saved by the Jesse Helms machine in North Carolina, which helped deliver that state and allow Reagan to remain competitive up until the convention... and which also depended, in part, on mobilizing diehard Wallace supporters to vote in the Republican primary. So, the Wallace factor took some time to fully get behind Reagan.
But imagine that, for whatever reason, Reagan absolutely crushes Ford in New Hampshire, forcing the president out of contention in the early running. With Reagan’s nomination all but assured, turnout is much lower during the Republican primary season. What are the knock-on effects of this? Well, it frees up many Wallace supporters to actually vote for Wallace in the Democratic primaries. In fact, the impact might be almost instantaneous. Look at the Democratic primary in Massachusetts - Wallace came within striking distance of winning that contest. One would not need to shift that many voters to his column (perhaps unaffiliated but culturally conservative blue collar voters) to give him the victory. Sure, Wallace would not win that many more delegates, but it would surely be a result that generates much media attention and build him momentum. That, plus the Wallace voters in Southern states who would have no need to strategically back Reagan, could help make him knock out Carter early on and become one of the frontrunners. Now, it is admittedly something of a leap from “one of the frontrunners” to “Democratic presidential nominee”, but the scenario positions Wallace to be a serious contender.