Here's a wrinkle suggestion that might work...
I'm on a planet, looking for elements in my SRV. Typically I'll ignore the cargo canisters, but I'll usually go investigate if the scanner indicates escape pods. Since big brother at the Pilot's Federation is peering over my shoulder in real time they should know when I call the ship down and load all eight pods, download the barcode data as they come aboard and instantly know who's in them, what ship they were on, where and when it went missing and if they're deceased.
**Incoming mission critical message**
CMDR, we've been advised you've found a couple of escape pods we're very interested in getting our hands on as soon as possible. We don't care what you do with the passengers, but we are willing to offer you a one million credit bonus, EACH for the captain and first mate. The condition is, you must get them to station x in system y within one hour.
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Accepting this mission marks two of the eight escape pods in your hold "Mission Haulage", adds destination text and a countdown on the inventory item itself, as well as adding a confirmation in the comms panel and a mission entry in the transactions tab with the same timer, destination details and a show on galaxy map button for easy route plotting.
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**Incoming mission critical message**
CMDR, we've intercepted your comms and would like to make a counter offer on all eight of the pods in your hold. The two you've heard about are wanted human traffickers that kidnapped one of our science teams with the intention of... Well, you probably don't want to know. We can match their bonus, 250,000CR for each pod returned to us at x in y...
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Accepting the second mission cancels the former, and annoys them enough to send a couple of cleaners after you.
Cancelling the second mission and proceeding with the first spawns supercruise NPC's trying to intercept / hyperdict and otherwise stop you getting to the delivery on time but if you make it to the right system the cleaners mentioned above will spawn and help you fight off the second party and provide some dialogue on punctuality or lack thereof.
Rewards for making the delivery just after the hour could drop by 5% each minute to a minimum 50K after 20 minutes
Rewards for the science team may be increased by the first party, due to what the second party said about their value
Alternatively, both missions could be cancelled at initial offer and the local military might show up to try and terminate the pair of wanted criminals you're harboring, unless you eject them.
Salvaging any mission class item that you don't already have a mission for could trigger incoming dialogue, fleshing out the search and rescue dynamic while still making use of the current hand in window. Some items may only pay a surprise bonus when handed in, regardless of where. Commodities could also spawn missions, especially if you stole unique haulage.
It's not just the missions that show up on the board that need some love and attention.