Engine Oil

if you have low oil pressure heavier weight oil is only a band aid so 20w50or straight 40w 5 qts with filter will help maybe maybe not, usually it's time for a rebuild when low pressure show up.

sending unit ?

From experience, the automotive sending unit will read basicly nothing or be topped out.
Was the oil pump replaced during the rebuild? Journal bearing? Or just the heads? Check with the rebuilder.

15 psi at idle and 45 psi underway may be about all you can expect from a Ford.
SAE 40 should give you the highest preasure. Just let it idle until it get up to temperature before puting the coal to it.

You have to verify what the actual pressure is first. The only way to do this is with a mechanical test guage. You should never diagnose possible engine problems with the onboard guages.

i agree w/manual guage to check the true psi reading,as far as normal ford oil pressure,15 psi is not normal at idle.worn or incorrectly installed cam bearings are the bastard child of oil pressure.Oil pressure -hot@2000 rpm's40-60 lb's for a 302,40-65 lb's for the 351. Autometer makes a full manual guage w/20' of tubing,Sumitt, for about 75.00 bucks.you can kill two birds w/one stone.mt stroker has one,she shows 65 lb's cold idle,with 55lbs hot,15/40 Rotella. Ask your rebuilder about cam bearings and his clean work habits,did he build it on the floor?????