Slitherine

Flight I is described as setting a new Speed record up to Mach 5, but has the peak altitude step and graphic.
Flight II is described as setting new altitude record above 100 km but has the High Speed Leg step and graphic.
This also made me wonder if the badges associated with Flight II were meant to be associated with the Altitude mission or just with completing all missions.

I agree, there is definitively some crossing between the two flights. Historically the X-15 set an altitude record of 107 960 meters the 23/10/1963 (that would be Experimental Flight I) and a speed record of 7 272,68 km/h the 3/10/1967 (Experimental Flight II). The first test flight was in 1959, so the program is a bit early in the game.