I think it depends on what the 360 currently has whether a 5.9 Magnum might be the way to go. If the 360 is bone-stock with some cylinder bore wear I'd pull it and have the bores sonic-checked. Supposedly the first few years of the 360 used the same casting cores as the 340 so with the bores being .040" smaller you get that much extra wall thickness to play with which makes them the best for a max-effort build. If the 360 LA checks out good with a compression test I'd just put in a cam, intake, headers etc. and have fun, 400 HP should be easy even with stock 8.5:1 (or less) compression.
Magnums are a great option, I have a 5.9L short block in my Duster with a custom-grind Racer Brown hyd roller cam and reused the stock roller lifters. Gotta make sure the top end setup works for it though, I put LA-based Edelbrocks on mine (long story) and had to devise an external oil supply to get oil to the rocker shafts (Magnums oil through the pushrods). If you find an earlier (pre-1997 or so) Magnum block they usually still have the oiling hole drilled in the block to oil LA shaft rockers so that becomes a non-issue, run whatever heads you want in that case! You can also run an LA flat-tappet cam and lifters in a Magnum block with no issues.
