Alder, maple, ebony could turn out as a bright, percussive guitar, but I heard alder bolt-ons that are quite neutral and sometimes even middy. It's a bit of gamble. Nevertheless the Abraxas is a good middle of the road here: some extra mids, less highs and a bit more compression than the Mule. For the neck I would pick an Irish Tour, that also matches if you want to split the Abraxas.
I have IT's paired with a Crawler in a swampash/ebony board-strat. Great combo for a lot of styles. The Irish Tour-neck has that woody vintage character, but with more bass, mids and a tad less topend than the Mother's Milk. They're grittier and handle (loads of) gain with authority. Clean the neckpickup sounds very good too. From RHCP to SRV to (hard)rock, the IT will deliver.