You really need
a tach. ESCs are notoriously non-linear so 10% or 20% *throttle* tells us nothing about the rpms you are really running at. I use a "rule of 10" for a *ballpark* ratio of feedrate and cutter rpm... 600 mm/min for 6000 rpm. This results in 10 perforations for every millimeter of travel... and cranking the cutter speed up to 9000 rpm (15 perfs/mm) is about as high as I would ever go. Typically, as I use a servo tester in conjunction with my tach, I pass through 6000-8000 rpm in the first 1/4 - 1/3 of the servo tester's dial markings, using a 1100KV motor at 12 volts (theoretically 13200 rpm, max).
I don't know what motor and voltage you are using but the needle "blur" in your 2nd photo shows you are definitely running too fast... and the mass of the unsupported needle is being forcefully thrown outward with each change of direction, resulting in the "bulge" in the blur. Further, if you are running at 20 mm/sec (1200 mm/min) and nearly getting a decent cut, you are running double the values I recommend... probably close to 12000 rpm on the cutter.
I, too, used 0.025" piano wire for years on cutters dimensionally similar to Mark's Foam Ripper cutter and generally found the "sweet spot" for the cutter rpms to be in the range of 6000 to 8000 rpm. I know some people run faster/hotter than I've recommended here (especially in the ERC Timsav cutter "camp") but I feel it puts undue stress on the cutter's bearings and needle and probably shortens their life. It also results in more friction heating in the Mig-tip needle guide. So my recommendation is getting a tach like the one linked above... but at the very least I'd slow down back down to something in the 600-800 mm/min feedrate and ~10% "throttle" setting you were using and get more of those "works great" experiences. A little patience goes a long way...
-- David