Slow shifting can make noises. Fast, firm shifting especially to R is what it takes. Shifting is only done at idle RPMs which Merc specs on my engines 675 RPM +/- 50. Faster idle just makes sifting harder and easier to tear up your lower unit.
Caution must be exercised when shifting into R, unlike F as a straight up alignment of a square cog (actually 3 on some engines and 6 on others) on the movable shifter "clutch dog" that is positioned back and forth along the prop shaft engaging a square socket on the rear of the R gear and a sawtooth (easily sifted with the engine off) on the rear of the F gear. If you try to force the shift to R and the pins and sockets aren't lined up and you apply pressure you can bend the shifting mechanisms both in the engine and/or in the remotes.
Yes you can shift with the engine running on muffs with running water for cooling. If the engine is off and you want to shift into R you ease into that position till you feel a bit of resistance and with that light pressure manually turn the prop till the shifter goes on fully into R......that may take 2 people if doing it from the remote control with them hooked to the engine.
Your findings on your oil drain are good news. If you have problems it will be in linkage, either internal or external.
Walmart sells Mercury/Quicksilver high performance oil in the sporting goods section. A quart bottle with a pump and hose adapter make a sweet job out of something that could be a messy PIA. Remember you pull the drain at the bottom of the gear housing, and vent plug(s) on the Port (left) side of the engine just above the Anti-ventilation plate and drain all the oil out ........with the engine vertical.
Then screw in the hose adapter (that came on your bottle of LU oil) into the lower drain/fill hole and pump the handle till oil comes out the upper vent(s) ........with no bubbles. Insert the vent screw(s) and tighten and then remove the hose from the hose below and quickly install the drain screw and tighten. You will loose a little oil in the plug replacement but strive to minimize the amount.