It's been 13 years since I put together that 360 LA with Magnum heads but from what I remember I didn't get oil to the rockers just from priming. Since you have roller lifters and don't need to break in the cam you could try running it without valve covers just long enough to confirm oil is getting up there. Just make some shields out of cardboard or other cheap disposable material to keep oil from splashing/dripping out.
How will you be tuning with the factory computer? Only asking because I don't have any experience with them lol. I have been able to tune the GM P04 ECM in my 2000 Buick with HPTuners but that's obviously not the same as Chrysler JTEC.