Would love to know more about what might be happening in the oil filter housing - any ideas?
Gonna start with what is probably obvious- O-ring on bolt, bolt into housing, spring on bolt followed by thrust washer then filter.
I'm looking at the Honda manual right now... The pressure switch should turn the light off at 7.1psi. And to quote: "When operating the engine under extremely high oil temperature (over 244F, 100C [sic]), the warning light may intermittently come on at idling speed (800-900 rpm), however, this does not indicate a problem."
And, "If the oil pressure is 50 to 64 psi at approx. 3000 rpm and the oil temp is 140F, the condition is satisfactory."
20w50 will give you slightly higher pressure.
So, to clarify, your light is now out and you have 10 psi with a warm engine at 1500 rpm? That sounds right. You haven't said whether you've revved past 1500 rpm to see if the pressure on the gauge rises. If you have access to compressed air, aim some into the back of your gauge- if it don't go above 10 psi- bad gauge. (I actually just tried this with keyboard duster stuff and got near 40 psi).
If you didn't replace the 3 o-rings on the ports of your new/ old pump, it'd be a good idea. Sometimes that alone will restore pressure. They are 20mm o.d. x 15 i.d. x 2.5 w. Same size as the filter housing bolt o-ring. Honda gets a ridiculous $4 and change for them so try a local rubber and gasket joint. Grainger has 'em.
And Ron means "exhaust tappet inspection caps". On the valve cover. Rockers are under there and you should get oil all over the front fender if yr top end is being properly lubricated with these removed and the engine running.