I think you are missing a fundamental aspect of strobes. They will all hold enough power for a single full power output, which is the same as two half power flashes, four quarter power flashes etc. So it is no coincidence you are getting 8 flashes at 1/8th power!
It has nothing to do with recharge times as no strobe will reenergize its capacitors in a fraction of a second.
If you want more flashes in a burst turn the flash power down to 1/16, then you will get sixteen flashes in a second, well something close to it but you will get some fall off. If your strobe isn’t outputting enough light at 1/16 you need to open your aperture, raise your iso, or get a more powerful (higher output) flash.
If your current strobes are 600ws then no 600ws flash, however much you spend, is going to give you 12 flashes at 1/8th power in one second, you need a 1,000ws strobe set to 1/16. If your current strobe is 200ws then any 600ws flash will give you the same power you have now but for 12 consecutive flashes in one second.