Barr may not have many fans here, but the DOJ is highly constrained in these matters by an inconvenient provision of the U.S. Constitution (from Article II, Section 1),Geez. I don't think anybody is saying that Barr should be involved in determining the electors.
It's the potential federal crimes that should be investigated.
If you want the DOJ to get involved, the easiest course of action would be to have GOP legislatures act to disqualify hundreds of thousands of ballots from Atlanta, Philadelphia, Detroit, Milwaukee, etc. — for violations of STATE election laws.
The DOJ would be involved as a matter of course over Voting Rights Act concerns.