I've done this modification on a number of guitars, specifically Ibanez RT models which I converted to AANJ style. On the RT mods, both the body and neck were originally square-heels. I've also put AANJ 22-fret necks on regular, square-heel strat bodies and modded the bodies to fit the AANJ contour. However, I haven't done this conversion using an AANJ 24-neck, so take what I describe below with a grain of salt.
This conversion requires that the corner of the body be cut/sanded/refinished into an AANJ-like shape. The most difficult part is getting the refinish to match the rest of the body without fully repainting the whole thing. The conversion also requires that the 4th hole in the body (the one at the corner you will be removing) is lost, so you have to drill at least one new hole in both the body and neck. Actually, because the AANJ pattern doesn't perfectly match any of the 4 holes in a standard body, I have always filled and redrilled all 4 holes in the heel of the neck to match the new pattern.
Is it worth it? As others have said, it can certainly be done, but it's far easier to buy a new neck from Warmoth or elsewhere.