Step 1: Combine whites, sugar, and salt in bowl of standing mixer; set bowl over saucepan containing 1 1/2-inches of barely simmering water. Whisk constantly until mixture is opaque and warm to the touch and registers about 120 degrees on an instant-read thermometer, about 2 minutes.
Step 2: Transfer bowl to mixer and beat whites on high speed with whisk attachment until barely warm (about 80 degrees) and whites are glossy and sticky, about 7 minutes.
Step 3: Reduce speed to medium-high and beat in butter 1 piece at a time.
Step 4: Beat in cream of coconut and coconut and vanilla extracts. Stop mixer and scrape bottom and sides of bowl. Continue to beat at medium-high speed until well-combined, about 1 minute.