Oil pressure dropping when you clean all the crap out of the engine is normal.
Oil is pumped from the sump through passages in the engine to places that need oil, such as camshaft bearings, crankshaft bearings, lifters, valves, etc., and the oil passes through those locations and leaks back down to the sump. When an engine is new, some of these locations are not seated yet, and oil goes through the gaps and to the sump pretty easily. Oil pressure can be pretty low. As you do your run-in, maintaining rpms to maintain high oil pressure and high oil flow, these surfaces seat and close up, less oil flows through them, and the oil pressure goes up. Over the life of the engine, as these surfaces wear and open up, more oil flows through them and oil pressure goes down.
This is one reason why an annual inspection on an airplane piston engine includes taking oil pressure readings.
You are measuring with the gauge the pressure the pump is supplying along one of the main routes within the engine. When the engine is full of garp, the oil passages are getting clogged up, and less oil flows, so oil pressure goes up. If you flush out all the garp, flow will be increased, and oil pressure will go down.
The rule of thumb is that you need to maintain 10 PSI of oil pressure per 1000 rpm on the engine. So idle oil pressure of 10-15 is fine, since your rpms are down around 600-800.
Going to heavier weight oil will give you higher oil pressure at the gauge, but it will also slow down flow rates at critical lubrication points. As long as you are maintaining 10 PSI per 1000 rpm, I would stick with 10W30.