I understand your issue is, your engine burns oil from the LH side upon startup. The disadvantage is, you really don't know what was done during the overhaul although you have great confidence in your builder. (We've been here before.)
Generally, there are a few causes for burning oil, IF that is what's really going on. I say it that way because we had engines that burned brake fluid 'in spurts' but the evidence left a low M/C fluid level in the reservoir.
Valve seals/sloppy guides are causes for burning oil. Improper cylinder crosshatch, a broken ring, a warped head or bad head gasket will also cause oil consumption. Excessive oil pressure might cause oil to blow past a warped head or bad head gasket, but that is rare.
Improper 'Y-Block' head bolt torque is common because the Ford Shop Manual gave incorrect torque requirements. In fact, the spec's were too high which caused many bolts to break, kinda like this one:
That condition mimics a bad head gasket or warped head. BTW, that white stuff is Teflon plumbing sealant because this bolt passes through a water jacket.
A standard Melling M-42 oil pump works beautifully in my 'Y' with no alteration. Melling is a high quality brand, used by most engine machine shops that offer a warranty.
Because of all the little idiosyncrasies of the 'Y', even a seasoned Chevy builder will miss a lot in building this engine. The same holds true for the FE. It's good to hear your engine is smooth-running but the real proof is in longevity. Without oil modifications, the timing chain and rocker shafts are starved of oil. Don't forget to add ZDDP to your oil for the solid flat tappets. - Dave