Mussaf RHI might be attributing these songs to the wrong people. I'm sure you can help out.
Note on the tunes: the first day of RH is Shabbos this year.
Melech Elyon - Ani Maamin Shehaborei, Dveykus
Chamol - Yedid Nefesh, Regesh
V'Chol Maaminim - Avinu Malkeinu / Yedid Nefesh, classic (like they sing in the Young Israels on leil Shabbos)
Heyei Im Pifiyos - Shomrai (starts from Horeim)
Hayom Haras Olam - Yedid Nefesh, MBD
Areshes Sefoseinu - Yedid Nefesh, classic (see above)
Hayom Tiamtzeinu - Mizmor LDovid (the one Shmuel Kunda A"H used for his Shabbos Zemiros song)
Kaddish Tiskabel - Lo Sevoshi, Shlomo Simcha