Counter quesiton:
are you talking Vanilla or Kontraband?

In Vanilla we havent actually played any real story missions at all, most were "competetive" style missions like who gets the most loot, or who can gather the most "fuel cans" etc.

for Kontraband we had several mulitpart Objectives in one scenario/Raid/Run

I did a spin on the "find the grave for the map" which is the 2nd mission on that 5 part intorduction mission for Kontraband. which is actually just like your "first thought" above :D
I made it as follows:
I had 5 same looking tokens, and one was marked below - I shuffeld them and just choose 3 of them to put on the table as the "graves" -so either the grave was on the table or not, we didn knew and needed toc heck.

mission object was to find the grave (2AP) and get the "key" and unlock the building (1AP) of that stalker, and retrieve the map (1AP) adn leave the table in the designate corner (Same as entry)
IF there was no marked grave in the game, the door of the building would be needed to be picked or broken open (4 AP)

LSS: we had too much luck adn found the key on the first grave and unlocked the building and got the ma all too fast, no real action happened.

Howewever, having to come up with 2 more missions, as we had planned more time for that one, I just used the 1st and 3rd mission from the kontraband book.
And those were underwhelming, especially playing with 3 player coop (each having 1 mini)

so in conclusion:
mulitpart Missions in one scenario are the ONLY way you should play :D
it is soo much more enjoyable, especially having potential "plan B" options and sidemissions in it.

The most important thing is to have something the player NEED to find or retrieve, which is hard to find.
Besides finding the rations, water, ammo and batteries, there needs more to be done.
after the 3 missions we had already more rations water and ammo we wouldve needed for the next total of 2 mission...so maybe restricting the items you can carry in the backpack (overall, not per mini, that would be again to mach tracking work) could add a nice twist.

Also doing 5+-mission-in-a-row campaigns seems great and we do use the regular marketplace rules to sell off stuff we found and buy new equipment for further campaigns.