here's my take... 10w40 is a bit of a junky oil when it comes to viscosity swings.. but has it's uses.
I see 4 things you could do.
1, swap in a new oil pressure gauge if it's not a newer one. old gauges can be inaccurate.. even 4 psi off is huge where you are at on pressures.
2/3, if gauge is good, you -could- go to a thicker oil.. it will up pressure a bit.. but is a bandaid. then again.. a cheap and easy bandaid too. 15w40 is a high quality oil as it is c rated... 20w50 is your other choice.
4, as said.. a quick way to up the pressure is a poor mans rebuild. drop the pan and swap in rod and main shells of the same size it already has. no need to even plastigauge them.. the old ones fit when new, and have worn from there.
that will get you some... and is fast and easy. reworking the oil pump is a great idea.. but takes more tools than the average shade tree has. bushing remaers.. etc. and if the pump needs changing.. you have to line bore as it is the front cap.... so may / may not mess with it.
If you are in that far.. might pay to pull the head, hand lap the valves,ream the ridge at the top of the sleeves, adn then put in new rings. that poor mans upper and lower will take a day, and requires no real special tools.. the ridge reamer and spring compressor can be rented at most auto parts stores..
you will get a compression bump, and a few psi oil pressure. might hant to run a brake or cyl hone into each jug up and god for a lil cross hatc for a couple seconds to helpt he new rings seal..