Passenger car 4 speed shift linkage mounts on the very rear housing of the transmission. That makes it very close to the stock seat.
Most 3 speed conversions have the same problem. Some on this site have car 4 speeds, perhaps they can give some guidance.
It's not easy or cheap to fix "modifications".
Fred


1956 3100 Pickup/Red/350/3sp OD/PS/Disc Brakes
1957 Bel Air Sport Coupe/Red/355/TH350/PS/Disc Brakes
2017 Silverado LT Single Cab SB/Black/5.3/6 Speed Trans
1947 Willys CJ2A w/F-Head engine