He directed VF4 and Psy-Phi (if anyone was lucky enough to play that one before it got recalled and cancelled) after he was done with Shenmue . Around the same time as directing Shenmue 1, he also directed F355 Challenge [both this and Shenmue came out in the same year!], so he seemed to be capable of juggling multiple projects at once.
It certainly seemed like he was responsible for VF4, but in the 20th Anniversary Interview it seemed like he had done everything with the series with the series since 3.
VF4 is the entry most praised for its depth balance and the like, which is mostly attributed to Kataoka who installed internet infrastructure for Japanese arcades in the early 2000's, which further enhanced competetive aspects and the like. Suzuki's desire was to make it more simple rather than a "e-sport" like.
Psy-Phi never did do much for me sadly - Suzuki said it was ahead its time, but I disagree. Touchscreen in arcades weren't new in 2006, and it just seemed like Psychic Force from Taito.