Very easy to implement secondary objective - lockboxes
This is very simple secondary objective since many features already exist.
Firstly generators are now repaired at significantly lower speed until survivor instals into them new item called Spare parts. These spare parts can be obtained from lockboxes (special kind of chests) that are randomly spread around each map but unlike chests they are locked.
Similliar to lockboxes new type of keys are also randomly spread around the map which are called lockbox key and they are 1 time use keys for unlocking lockboxes to gain 1 unit of spare parts that can be also used once to make generators repair speed normal again for that specific generator. There are 7 lockboxes on each map but slightly higher amount of keys since they would be very easy to miss.
This would create new objective for survivors that is very stealth based and would drastically decreased cases of 7 and less minute matches while still letting generators to be the main objective.