Fair Value Measurements - Carrying Values and Estimated Fair Values of Other Financial Assets and Liabilities (Details) - USD ($) $ in Thousands	Jun. 30, 2022	Sep. 30, 2021
Carrying Amount
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Notes payable	$ 1,049,078	$ 1,054,030
Carrying Amount | Senior Notes and Term Loan
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Notes payable	977,325	983,827
Carrying Amount | Junior Subordinated Notes
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Notes payable	71,753	70,203
Fair Value
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Notes payable	891,224	1,117,168
Fair Value | Senior Notes and Term Loan
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Notes payable	819,471	1,046,965
Fair Value | Junior Subordinated Notes
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Notes payable	$ 71,753	$ 70,203