(June =4%, July =6%, August = 26%, Sept = 39%, Oct =20%, Nov = 5%)...

1991-2020 Average number of Hurricanes: 7.2 (black)
2022 Forecasted number of Hurricanes: 10 (Red)
Plotting distribution of 'hyperactive' years:
(1969, 1995, 1996, 1998,1999, 2003, 2004, 2005, 2010, 2017, & 2020)

Note that many of these years are indeed very back-loaded (1969, 2005, 2010, 2020) with very active late seasons.
Some follow the historical distribution (1995, 2004).
The Average distribution of these hyper seasons (Red)
Comparing the 1991-2020 Average season using historical distribution (black),
2022 Forecast using historical distribution (green), and
the ave. distribution of hyper seasons (red)....

draw your own conclusions, but it appears the hyper seasons tend to be back-loaded, (but not all back-loaded seasons are hyper).
The distribution of Hurricanes (front-loaded, normal, or back-loaded) are relatively independent of activity levels, but (on average), hyper seasons appear more active than the baseline for each of the six months, especially October.