I’ve said the same thing (except the 2/3 vs 1/3 aspecf) several times on J-L when people dismiss the bypass system. Jag designed a positive displacement system adequate to feed 12 big ends, seven mains and the cams at idle. This inevitably means massive oversupply at high revs when you need the cooling most and the bypass works best. When cold they used the integral oil/water heat exchanger and filter to warm the oil via coolant on the first twelves (E-Types) and altered it on the sedans because the subframe got in the way of that packaging.
I would be careful with hoses and coolers (5/16 sounds very small) because I believe many coolers are only rated to circa 5 bar. My D uses dry sump full flow cooling with the factory oil rad certified to that figure. 5 bar /70 psi is plenty for the air/oil mix in the scavenge circuit (analgous to the bypass) but would be risky low for cold oil on the feed circuit, needing careful and prolonged warming up before using it in anger.