The arabs themselves never wanted to be called Palestinians - they used the name "Syrian Arabs". Yassir Arafat, former leader of the PLO, was one of the most prominent opponents of the word "Palestinians" with regard to the arab population - he only changed his mind as Jordan and Egypt signed a peace treaty with Israel, because he wanted to distance himself from these "traitors".
One of the problems he (and also most arabs) had with the word "Palestina" - it has exactly ZERO relationship to arabs and to Arabic languages. It's a greek word with actually Hebrew roots. It means "land of the Philistines" - and the Philistines, according to many historians, are a mixed group of people, mostly from western Mediterranean (modern-day Italy, France, Spain, northern Africa), also called "the sea people", or, in other words - pirates. The Romans introduced this name to the region to wipe out the original names Judea and Samaria (which IS actually a sign of a genocide).
And now to your points - the word "Aschkenaz" IS actually of middle-eastern origin. It describes people who lived in the area of modern day eastern Turkey, north-eastern Syria, and north-western Iran - similar to the area where Kurdish people live today. The meaning of the word changed over time, and yes - nowadays it does have some relationship with Europe - it describes Jewish people who were driven out of Judea and Samaria by Romans and later settled in the middle and eastern Europe. So - yes - they are by definition Palestinian refugees with a right to return to their native lands.
But, of course, they are only one group of the Jewish people and not even the only one who lived in Europe. There are also displaced Jews and their descendants in Irak, Iran, northern Africa, India, even in China and Japan. But in the end, every one of them, including the "European" Aschkenazim still have substantially better claims to the land of Israel than the Arabs who are by definition just invaders in that region.