You really haven't been cycling the 75G tank very long though it is possible that the cycle is started but may not be finished yet since you have added some amount of cycled media from the existing 10G tank.
Have you been keeping a written log of your water testing results for ammonia, nitrite and nitrate? If so, post when you started cycling the 75G tank and what your test results have been by the date you tested.
You should have zero ammonia, zero nitrite and some level of nitrate above 10ppm for at least a week after the cycling process is finished.
Usually fish-less cycling uses some type of bottled bacteria, very mature media from a cycled aquarium, the transfer of the existing filter with its mature media to the new tank or clear bottled ammonia from a store.
No reason to start another topic and ask similar questions on if it's OK to move the fish, much better to ask in this topic since all the relevant information will be in the same place.
I know you are excited about the new tank and moving your fish so I'm not trying to be mean here. ?
In both cases I have never had them explode though that may be due to the composition of the Feather Rock or just my good fortune.