YouTube recommended that video to me for some odd reason. After picking my jaw off the floor, I realized that in the context of the 1950s, it's not as mad as it seems. Long range cruise missiles were launched the same way. Turning a Starfighter into a manned SAM must have seemed quite logical.
SM-62 "Snark" (turbojet sustainer):
CIM-10 "Bomarc" (Ramjet sustainer)
mgm-13 "Mace" (turbojet sustainer):
Blue Angels support C-130 "Fat Albert" with JATOs firing...
Much cleaner propellant than that big JATO on the F-104.