Swapping tyre will hardly make a difference as the overall difference is negligible. Not worth the effort in my opinion. Linear start assist in Grande is not a Launch Control, in drag race at full throttle from the get go, it won't make any difference either. Some features are just gimmicks, just like sport mode in Grande.
Both cars are pretty much neck in neck in my experience with Grande usually being considerably slower after 190. The reason you felt Grande was quicker has actually more to do with its CVT transmission compared to Civic X's CVT. Toyota's automatic transmissions are a mile ahead of Honda's, even globally.
Regarding, how to "beat" Civic X in a drag race using a 8th/9th gen Prosmatec, it's simple. Start from roll on from 80 km/h and put the Prosmatec car in "2". The moment both cars floor down, Prosmatic will already be at a higher RPM, while Civic X being CVT will have to go all the way to redline. By 120km/h, traditional auto will be ahead. This is assuming 8th/9th gens are in perfect condition (cat, plugs, throttle body, tensioner/adjuster, etc) since alot can go wrong with R18 engines as its mileage increases.
Result will be opposite if you race a CVT car against Prosmatecs from stand still.