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I'll assume you've checked the PCV system and temporarily installed a dedicated oil pressure gauge at the OEM OP sending unit port?
I've gone through DIY installing a Ford reman'd 5.4 but don't know I'd recommend that without a few caveats being known up front. The biggest issue for me was warranty coverage. its NOT a simple process but does work. Details upon request, I might have a link to a write-up of sorts I've posted here on FTE.
Frasier is another name I've seen mentioned here but have nothing more information wise about their products or warranty coverage. Jasper really isn't perfect and can have their own issues BUT if you have one of their authorized re-sellers install the engine and there's documentation to the sale/install chances are you'll not encounter a bunch of BS with that process.
Ford's big rebuilder here in north Texas is AER. We had an AER 4.2L rebuild stabbed into our '97 F-150 when the original broke a rod at 92K. The AER rebuild was still running strong when we sold the truck at 225K... so 133K on the rebuild.
I ended up with a Jasper due to availability. Little over a yr and alls good. Mixed reviews with all of em. Trust your installer and let him know if it ain't right you'll be back. Good Luck.
Just to bring a close to this, I too went with Jasper. After looking at every vendor I possibly could, Jasper’s was not only available, but also the best choice.