Hello Mike,
Z240 recharges 1-2 seconds after energy-intensive Canon double flash, but not TTL-Converter. Double flash includes Pre-flash + main flash, with very short interval between them. Such double flash discharged Z240 capacitor significantly. Z240 requires recharge before next TTL shot for getting required lighting accuracy.
Bigger size strobes (for example DS-161 or YS-250) don't have such effect, because of large capacity of main capacitor and a bit different control logic. Using those strobes, it is available to get enough quantity of shots in fast series at the same TTL configuration.
So, the effect refers to underwater strobe specific.
By the way, Nikon TTL doesn't have such significant effect with Z240, because of shorter Pre-flash than Canon in underwater systems.
Canon TTL camera needs to receive back significant energy Pre-flash for accurate and stable exposure rating, it becomes more important underwater than on land, because of absorption of pre-flash by water. Canon camera TTL measuring system is less sensitive and stable than Nikon, unfortunately. That is why the large energy Pre-flash for underwater usage was a forced decision for TTL-Converter for Canon. Using that solution, UW Technics has reached high TTL accuracy and stability underwater for Canon cameras.
Of course, you can try Canon TTL circuit from any other manufacturer. Maybe, it will have a shorter Canon Pre-flash, which would be better for fast serial shooting with Z240. But you have to compare the TTL accuracy and stability in this case. Don't forget that flash exposure accuracy is the main task for TTL.
If you interested in continuous (serial) shooting, look to User's Manual of your board, - for getting stable flash exposure at fast continuos shooting with underwater strobes, it is recommended to switch system to "Manual" mode (by camera menu, or by strobe switch). This case you exclude Pre-flashes, make underwater strobe recharging faster. Using Manual mode and small strobe intensities, you can get a lot of shots in fast series.