Lots of performance parts on my LA 360 - let's build my Magnum / Stroker

The first question is there something wrong with your current LA that you need to change it for some reason. It sounds like it has a good solid build, and the Magnum block is not going to gain you anything. The one good thing about the Magnum block is it is set up to run a hydraulic roller, and your LA already is set up that way. Your LA heads will not work on that era of Magnum without some work to the oiling system for the shaft mounted rockers of the LA. The Magnum oils through the push rods for the stud mounted rockers, where the LA oils through a passage in the block and head to the shafts. You can run a oil line from the oils sender hole and T if off through the back of the heads, or there a couple of other ways to route the oil. Personally, if you LA block is still usable, I would do what machine you need to, and throw the stroker kit in. You will end up trying to make your Magnum into an LA, and you already have one without the hassle.