Credit Facilities - Narrative (Details)	3 Months Ended	9 Months Ended
	Jun. 30, 2023 USD ($)	Jun. 30, 2023 USD ($)	Sep. 30, 2022 USD ($)
Line of Credit Facility [Line Items]
Debt amortization fiscal year 2021	$ 14,250,000	$ 14,250,000
Debt amortization fiscal year 2022	19,000,000	19,000,000
Debt amortization fiscal year 2023	19,000,000	19,000,000
Debt amortization fiscal year 2024	23,750,000	23,750,000
Interest Rate Swap
Line of Credit Facility [Line Items]
Derivative notional amount	112,200,000	112,200,000
Interest expense increase (less than)		600,000
Interest Rate Swap One
Line of Credit Facility [Line Items]
Derivative notional amount	$ 16,200,000	$ 16,200,000
Derivative fixed interest rate	1.61%	1.61%
Interest Rate Swap Two
Line of Credit Facility [Line Items]
Derivative notional amount	$ 96,000,000	$ 96,000,000
Derivative fixed interest rate	4.10%	4.10%
Secured Debt
Line of Credit Facility [Line Items]
Long-term debt	$ 179,312,000	$ 179,312,000	$ 22,000,000
Secured Debt | Term Loans
Line of Credit Facility [Line Items]
Fixed charge coverage ratio		1.25
Debt amortization fiscal year 2021	14,300,000	$ 14,300,000
Debt amortization fiscal year 2022	14,300,000	14,300,000
Debt amortization fiscal year 2023	19,000,000	19,000,000
Debt amortization fiscal year 2024	19,000,000	19,000,000
Debt amortization fiscal year 2025	23,800,000	23,800,000
Voluntary principal amortization of term debt	3,600,000
Long-term debt	16,400,000	$ 16,400,000	0
Secured Debt | Term Loans | Excess Cash Flows Greater Than Or Equal to 2.50
Line of Credit Facility [Line Items]
Percentage of excess cash flow for each year of funded indebtedness to EBDTA		75.00%
Ratio of funded indebtedness to adjusted EBDTA, actual		2.50
Secured Debt | Term Loans | Excess Cash Flows Less Than 2.50
Line of Credit Facility [Line Items]
Percentage of excess cash flow for each year of funded indebtedness to EBDTA		50.00%
Secured Debt | Term Loans | Excess Cash Flows Equal to 1.50
Line of Credit Facility [Line Items]
Ratio of funded indebtedness to adjusted EBDTA, actual		1.5
Secured Debt | Term Loans | Excess Cash Flows Less Than 1.50
Line of Credit Facility [Line Items]
Percentage of excess cash flow for each year of funded indebtedness to EBDTA		0.00%
Ratio of funded indebtedness to adjusted EBDTA, actual		1.5
Secured Debt | Term Loans | Maximum
Line of Credit Facility [Line Items]
Ratio of funded indebtedness to EBITDA through maturity		4.50
Secured Debt | Term Loans | Maximum | Excess Cash Flows Less Than 2.50
Line of Credit Facility [Line Items]
Ratio of funded indebtedness to adjusted EBDTA, actual		2.50
Secured Debt | Term Loans | Minimum
Line of Credit Facility [Line Items]
Ratio of funded indebtedness to EBITDA through maturity		2.00
Secured Debt | Revolving Line of Credit
Line of Credit Facility [Line Items]
Line of credit, maximum borrowing capacity	70,000,000	$ 70,000,000
Line of credit, unused borrowing capacity	32,900,000	32,900,000
Long-term debt	$ 179,300,000	$ 179,300,000	22,000,000.0
Secured Debt | Letter of Credit
Line of Credit Facility [Line Items]
Line of credit, current borrowing capacity			$ 10,000,000