Replacement for 360LA

The balance between the 360's, LA vs. Magnum, are different. IIRC, there is a B&M flexplate to deal with this.

The question is, what is the budget?

IMO, rebuilding the "LA" would be a better idea and do it with new slugs that will be at or near zero deck for a great quench. The block may need to be milled to get to a zero deck height.

Since you have everything, a hone job may be it! Otherwise, a bore and hone, new slugs and rings with a balance job and a gasket set,,,,ehhh, throw in a new oil pump while your at it for a small fee, that is cheap as it gets.