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Long-Term Debt, Finance Leases, and Other Borrowings - Schedule of Long-term Debt (Detail) - USD ($)
$ in Thousands
Jun. 30, 2025
Sep. 30, 2024
Sep. 30, 2023
Debt Instrument [Line Items]      
Gross long-term debt, including current maturities $ 113,744 $ 315,210 $ 538,300
Less unamortized debt issuance costs   (2,395) (5,083)
Less notes payable warrants (774) (2,544) (4,913)
Net long-term debt, including current maturities 112,970 310,271 528,278
Less current portion, net of unamortized debt issuance costs (84,725) (50,455) (163,550)
Net long-term debt 28,245 259,816 364,728
Senior and Subordinated Notes Payable to Secured Parties, Due in Monthly Installments Collateralized by the Underlying Aircraft Through 2027 [Member]      
Debt Instrument [Line Items]      
Gross long-term debt, including current maturities     39,018
Notes Payable to Secured Parties, Due in Semi Annual Installments Collateralized by the Underlying Aircraft Through 2028 [Member]      
Debt Instrument [Line Items]      
Gross long-term debt, including current maturities   85,469 108,815
Notes Payable to Secured Parties, Due in Quarterly Installments Collateralized by the Underlying Aircraft Through 2028 [Member]      
Debt Instrument [Line Items]      
Gross long-term debt, including current maturities   73,884 90,401
United Bridge Loan Quaterly Collateralized By Underlying Equipment And Investments Through Two Thousand Twenty Four [Member]      
Debt Instrument [Line Items]      
Gross long-term debt, including current maturities     10,500
Other Obligations Due to Financial Institutions, Monthly or Quarterly Collateralized by the Underlying Equipment, Due 2022 Through 2031 [Member]      
Debt Instrument [Line Items]      
Gross long-term debt, including current maturities   4,681 67,637
Notes Payable to Financial Institution, Due in Monthly Installments Collateralized by the Underlying Equipment, Through 2024 [Member]      
Debt Instrument [Line Items]      
Gross long-term debt, including current maturities     1,075
Notes Payable to Financial Institution Due in Monthly Installments Collateralized by the Underlying Equipment Through 2027 [Member]      
Debt Instrument [Line Items]      
Gross long-term debt, including current maturities   0 41,098
Notes Payable to the UST, Quarterly Through 2025 [Member]      
Debt Instrument [Line Items]      
Gross long-term debt, including current maturities   113,656 139,100
Gross LongTerm Debt Including Current Maturities [Member]      
Debt Instrument [Line Items]      
Gross long-term debt, including current maturities   315,210 538,274
Notes Payable to the UST, Quarterly Through 2025 [Member]      
Debt Instrument [Line Items]      
Gross long-term debt, including current maturities 80,726 113,656  
United revolving credit facility quaterly collateralized by underlying equipment and investments through two thousand twenty eight [Member]      
Debt Instrument [Line Items]      
Gross long-term debt, including current maturities   37,520 $ 40,630
Revolving Credit Facility, Quarterly Interest Through 2028 [Member]      
Debt Instrument [Line Items]      
Gross long-term debt, including current maturities $ 33,018 $ 37,520