nice lookin' plant ....
roots look healthy - once the stems with rot are removed, I think your plant has a pretty good chance ....
allow any & all cuts to callous over before repotting ....
this can take several days to over 2 weeks depending on humidity ...... and I know its humid in Thibodaux
after pruning off rot - dust the entire plant with fungicide ....or use rooting hormone w/fungicide ....
place in a shady spot to air dry ...away from direct sun & rain
in the meantime ...mix up a batch of chunky + gritty potting media .... it should have more inorganic material - such as rocks & sand - than organic material - such as soil
once stems callous over - I would repot an inch or so below the green - exposing an inch or so of the white roots this is called lifting or raising .....
oh yeah ....don't expect anything to happen ..... adenium take forever to respond to changes
