It's possible that the solenoid might not be the main bottleneck in the speed, but more investigation is necessary to determine this.
I think this is very possibly the case. If you want to move the water faster you need to put pressure on the water, not just open the gate faster.
Some decades ago I was maintaining some Kodak machinery for making color prints from negatives. The machine would advance the negative and the paper and then the negative was scanned for color balance, exposure, etc. With that information a shutter and three color filters were swung out by their solenoids and then each color filter was swung in and finally the opaque shutter was swung in and that was the end of that print. The exposure times of each color were measured in milliseconds and were crucial for good print results. The machine could be doing over 200 prints / minute.
Due to filter lag the software would run a setup and measure how long it took each individual filter and shutter to move in and out after activation. Those values were then stored and used and taken into account by the software together with lamp intensity, color balance, etc.
It was essential that the filters move *fast* in and out. The delay was just compensated for in the software.
The machine was run by a minicomputer (this was before microprocessors) and the program was stored on TTY paper tape. Fun times!