A metal vane core or strut (64) is formed integrally with an outer backing plate (40). An inner backing plate (38) is formed separately. A spring (74) with holes (75) is installed in a peripheral spring chamber (76) on the strut. Inner and outer CMC shroud covers (46, 48) are formed, cured, then attached to facing surfaces of the inner and outer backing plates (38, 40). A CMC vane airfoil (22) is formed, cured, and slid over the strut (64). The spring (74) urges continuous contact between the strut (64) and airfoil (66), eliminating vibrations while allowing differential expansion. The inner end (88) of the strut is fastened to the inner backing plate (38). A cooling channel (68) in the strut is connected by holes (69) along the leading edge of the strut to peripheral cooling paths (70, 71) around the strut. Coolant flows through and around the strut, including through the spring holes.