That said, do you think there's any way that Humphrey might be able to dump Muskie for a moderate southerner without appearing desperate?
Appoint Muskie as Secretary of State? You're right in the implication that an incumbent President Humphrey no longer needs Muskie's
gravitas on the campaign trail in '72 and is free to seek a more strategic choice.
That being said, I'm not certain that a moderate southerner would actually
be a good strategic choice here versus Wallace and Reagan; HHH will probably run third throughout most of the South(*). Shoring up formerly liberal Republican strongholds in the northeast -- NH, VT, NJ, and DE -- is probably HHH's key to re-election, and Muskie (from Maine) probably helps there.
(*) One caveat: close three-way elections can produce weird results, like Bill Clinton winning Montana with 37.6% of the vote in 1992. So it's
possible HHH might get the odd state in the Deep South ITTL with something like 35% of the vote, but my guess is that he'd do
even worse than OTL '68, where he was held to under 30% throughout most of the Deep South. It's hard to imagine a southern running mate helping HHH enough to overcome those sorts of deficits.