I would check your oil pressure with a mechanical guage. Its possible that you have a faulty oil sending unit. Average oil pressure for a 3800 is around 40 PSI at operating temperature. The mechanical oil pressure guages are always the most accurate and will confirm wether or not you have a bad oil pressure regulator. Its very easy to change out the oil pressure regulator, should be less than an hour job. Just on bolt the oil filter housing and the oil pressure regulator valve is right there. Autozone sells the oil pump rebuld kit for less than $20, and the kit comes with a new pressure regulator and spring. If your going to rebuild the oil pump, then your going to have to remove the timing cover to access the oil pump gears.

Changed the sending unit, and no more erratic / high readings.

Good to see that the sending unit resolved your problem.