There were suprisingly quite a few V/STOL aircraft....here's some of them:
VTOL Experimental Aircraft PAGE
Couple more:
Army VZ Series PAGE
Here's the POGO
The SNECMA c-450
And the Ryan X-13
Just to name a few....
Ok, I will stipulate that these craft existed. But, I believe that I said "fully functional". Unless I am mistaken, we know of absolutely no VSTOL aircraft from that time period that would ascend vertically while shooting flames out the bottom and then transition (vector thrust) to horizontal flight that was either egg shaped or did not sport some wing like appendage.
The Ryan X-13 Vertijet flew only 2 times and only once where it transitioned from Vertical to Horizontal. Yes, that was in 1959. 5 years before the incident. But the aircraft looked exactly like an aircraft and the crew could not exit the vehicle without special equipment.
The Convair XFY-1 POGO was propeller driven. Like the X-13 verticle to horizontal transition was meant to be performed at altitude in a gradual manner.
I am surprised you didn't mention the Bell Convertiplane. It was very similar to the Osprey. But again made to transition at altitude in a gradual manner.
In VSTOL tech the transition from vertical to horizontal flight is a huge delimiter. There is gradual and there is nearly immediate. A great example of the nearly immediate is the Harrier Jump Jet and the Osprey. The transition from vertical to horizontal flight and the lack of lift sustaining wings are the real keys to wether this was or was not technically doable at the time. Personally, I don't think that it ws technically possible given the observed parameters.
1) vertical ascension to under 100 feet via some flame ejecting rocket
2) transition to horizontal at about 100 feet
3) no flame ejection in horizontal flight
4) egg shaped
5) retractable tri-legged landing gear
6) no wing structure to provide lift in horizontal flight
7) two man enclosed cockpit with entry port at the bottom of the craft
I can't tell you what it was but if the observations were correct then I feel certain enough to say that there was no known similar aircraft in the world at the time. That is fascinating to me.