"-hanger has been replaced"

Why? did it get bent ?
was it cracked after a bad straightening?
how long has the "new" hanger been on the bike?
hangers get bent from forces applied via the DERAILLEUR....

how sloppy is the derailleur?
do the shifts ever "stumble around" before they happen... a noisy delay before shifting?

frankly, TWO gears not available, sometimes.... sounds like a shifter issue.. what lube has been applied to the shifter? Shimano shifters can be affected by temperature when the Factory Grease gets thicker or thins out because of Ambient temps........ i clean and re-lube many mtb shifters here... there are not very many road bike riders, locally, but i've also cleaned/lubed several road brifters..... "it works one day., then acts up the next!"

another thing to think about... i've found a single strand of Cable inside a brifter before.... just one... about an inch long... it drove the owner absolutely nuts for around a year....

could you swap on a loaner brifter as a test?
leave the bar tape off for the test.. fresh tape is always encouraging anyway, right?