You say the waterpump pulley wobbles some on start up and then goes away. Take the belt off, grab the fan and see if it wobbles any by hand. Any wobble at any time is concerning. Plus... a 3/8 belt will bottom out on a 5/8 pulley.
~~ Jethro 1954 3100 Back to Life In the Dity Gallery 1951 3100 (gone) / 1956 4400 (still in the neighborhood) / 1957 6400 with dump body (retired) / 1959 3100 panel (in the woods junked) / 1978 Custom Deluxe K10 / 1993 S-10 4.3 / 2004 Chevy Crew Cab / 1945 John Deere H / 1952 John Deere B / 1966 John Deere 2510 / 1967 John Deere 1020