The only time Indy tales intrude on each other is when huge blocks of time are commandeered for no reason ("I spent a year searching for that..."). There's not yet been a need to address the EU because when Indy 4 was released everything after 1950 was a blank slate, and now we don't know what happens after 1958. Sorry Stoo, but while Old Indy exists in the Indyverse, he's a bit confused.
My hope is before throwing anything out they consider establishing an unreliable narrator. Curt Henderson from American Graffiti, who attends an unnamed east coast university in the 1960s and becomes a writer, seems the perfect character to tell Indy's tales using the scattered resources available to him. He might even embellish for his audience (including Old Indy!) or make up minor stories from whole cloth.
If they reboot in the 20s, then we'll cross that bridge later.