After referencing this article on Apple: https://discussions.apple.com/thread/8509743 and going through all three of that thread's recommendations:

1. Enable secure token in Terminal using the command: sysadminctl interactive -secureTokenOn -password - This threw the following error: 2022-10-20 11:00:27.406 sysadminctl[1137:7904] setSecureTokenAuthorizationEnabled error Error Domain=com.apple.OpenDirectory Code=5101 "Authentication server refused operation because the current credentials are not authorized for the requested operation." UserInfo={NSUnderlyingError=0x600000c41350 {Error Domain=com.apple.OpenDirectory Code=5101 "No existing unlock record" UserInfo={NSDescription=No existing unlock record}}, NSLocalizedDescription=Authentication server refused operation because the current credentials are not authorized for the requested operation., NSLocalizedFailureReason=Authentication server refused operation because the current credentials are not authorized for the requested operation.}
2. Toggle FileVault on and then off again. - Filevault would not enable, so the first part of that sequence can’t be completed.
3. Use the MacOS Setup Assistant to create a new admin account by deleting /var/db/.AppleSetupDone - This was the first thing I tried; but the resulting admin account either didn’t generate the token or could not set it to On as it should have.

After all three of those failed, since I didn't need anything on the MBP's internal SSD, just get it deployable, I booted into Recovery, deleted the Boot volume, created a new Boot volume, and installed Monterrey into the new APFS volume. This apparently corrected whatever was at fault in BridgeOS, as the 501 admin account was recognized by the Startup Security Utility as an admin, and FileVault could be enabled normally.

After referencing this article on Apple: https://discussions.apple.com/thread/8509743 and going through all three of that thread's recommendations:

1. Enable secure token in Terminal using the command:

   sysadminctl interactive -secureTokenOn <user name> -password <user password>

   This threw the following error:

   2022-10-20 11:00:27.406 sysadminctl[1137:7904] setSecureTokenAuthorizationEnabled error Error Domain=com.apple.OpenDirectory Code=5101 "Authentication server refused operation because the current credentials are not authorized for the requested operation." UserInfo={NSUnderlyingError=0x600000c41350 {Error Domain=com.apple.OpenDirectory Code=5101 "No existing unlock record" UserInfo={NSDescription=No existing unlock record}}, NSLocalizedDescription=Authentication server refused operation because the current credentials are not authorized for the requested operation., NSLocalizedFailureReason=Authentication server refused operation because the current credentials are not authorized for the requested operation.}

2. Toggle FileVault on and then off again. Filevault would not enable, so the first part of that sequence can’t be completed.

3. Use the MacOS Setup Assistant to create a new admin account by deleting /var/db/.AppleSetupDone This was the first thing I tried, but the resulting admin account either didn’t generate the token or could not set it to On as it should have.

After all three of those failed, since I didn't need anything on the MBP's internal SSD, just get it deployable, I booted into Recovery, deleted the Boot volume, created a new Boot volume, and installed Monterrey into the new APFS volume. This apparently corrected whatever was at fault in BridgeOS, as the 501 admin account was recognized by the Startup Security Utility as an admin, and FileVault could be enabled normally.