I would just like to know - is there a mesorah for Tehillim trop for Ashkenazim? I know that there is a Sefaradi one (I have heard them) but I would like to know if there is any Askenazi one. Thank you.
There was an Ashkenazi Tehillim trop mesorah, but it was lost about half a century ago:
R' Yisroel Rabinovich of Monsey, NY, is a master baal koreh and baal dikduk. He told me that as a young Yerushalmi boy, he met the last living man who knew the Ashkenazi cantillations for Tehillim. Unfortunately, at the time, neither R' Rabinovich, nor anyone else around, was interested enough in kriah to take note of this mesorah.
There is an ashkenazi trop for Tehillim, Mishlei, and Iyov (טעמי אמ"ת) but it was reconstructed from the Sephardic tradition. KAJ in Washington Heights chants Tehillim 29 with that trop on Friday nights. You can buy software to learn Ta'amei emet, and find sample mp3s from the software here.