There are no real examples of “minhag trumping halachah.” I wish people would stop trying to invent them here.
Mik:
Those who don’t learn Torah on nittel nacht still say the Shema and are technically learning Torah (if it really “trumped halachah” then they wouldn’t even do this).
About the brachas hashachar, perhaps the Shulchan Aruch HaRav says otherwise?
The Sukkah thing is interesting. I noticed that in the Kitzur he says that people started neglecting to sleep in the Sukkah, so poskim used a technicality of say it’s mutar so that there wouldn’t be so many people blatantly violating halachah. I assume this is where that minhag came from.
Washing for seudah shlishi is not, by any stretch of the imagination, “halachic.”