It is "very" easy to resolve this without actually reducing your hang time and removing courtesy tones etc.

Simply add - or reconfigure- the TX PL for the repeater transmitter so it only transmits PL when your repeater receiver is actually active. This can be done by using the COS or COR of your repeater to trigger the PL encoder.
If your repeater currently uses PL possibly this is an option in the controller set-up?

Now your PL'd link radio should only feed the IRLP COS when a valid PL is present. Your node will now only transmit to the IRLP network when someone is actually talking on your node.

Very simple and very effective and no changes need to be made to the hang timer, courtesy beeps or CWID as none of these will make it to the IRLP except for the occasional CWID that may be transmitted while someone is actually talking on your node. (This is permissible)

Post a help request to the IRLP Groups.io group if you have trouble with this configuration.