Hi Nwf,
Yes temperment genetics are passed on by drones (paternal side), hygenic genetics are passed on by queen (maternal side).
A few ideas:
Raise a lot of drones from your gentle queens to help with the statistical chance of getting those genetics into your virgin queens.
Merge 2 of your hot hives (pinch the queens) with your gentle hives so any young bees born after the pinch are from your gentle queens.
Then you can resplit them later. I think you surest way is to get mated queens from gentle stock, and introduce them. Its hard to get rid of local drones that carry hot temper as they can live the entire season. once your stock is all gentle, only then can your splits have a good chance of keeping their calmness.
I too had a hot hive -30 bees flying out as soon as I gently cracked the lid. Not fun. On the flip side, it was a very vigorous, healthy and prolific hive, but you have to do your tradeoffs I bought a mated queen and replaced the hot queen. I am still buying mated queens and nucs this year, and hope to have all good genetics to start my own splits next year.
Hope this helps.
Mart.