Declaring Desires:
You mentioned your desired solution should be not too long, not too boring, using mostly roleplay or non-combat related interaction, and without too much dice-rolling.
Barter Method
This suggestion is that you go the route of many famous computer games that are usually referred to as Quest, Adventure, or Point-and-Click. This method would require you to setup the story such that each quest item can be obtained be either completing a small task, or trading another item for the quest item. Each task or item required to obtain the quest items might lead to yet more tasks or item trading. In this method the players should be more or less aware of where the quest items are, and who they must get them from, and the game or story becomes completing the tasks and obtaining the items.
Fulfilling the Requirements:
- Not Too Long: You can design this in such a way to be as long as you want it to be, by increasing or decreasing the number of tasks or item exchanges needed to get the quest items.
- Not Too Boring: If you introduce enough variation into each task or exchange then the players won't get bored.
- Roleplay: Since you are writing these missions, you can control their content, and in such a way you can direct the game to be as violent or peaceful as you want.
- Dice: Again, since you are controlling these missions, you can simply decide to play them as a story, and just talk to your players about what they will be doing - hopefully since this method is not part of the mechanics of your system, there will be rarely an occasion to roll any dice - but many players may desire to roll dice to accomplish parts of the missions or to try to convince characters to lesson the cost of the exchange or the difficulty of their tasks.
Treasure Hunt Method
This suggestion is that these items are known to exist, but their whereabouts are unknown. The players must search for the quest items and retrieve them, usually by solving some kind of riddle or challenge. (Think Indiana Jones)
Fulfilling the Requirements:
- Not Too Long: You can design this in such a way to be as long as you want it to be, by increasing or decreasing the difficulty of the riddle or challenge for each quest item.
- Not Too Boring: If you introduce enough variation into each riddle or challenge then the players won't get bored.
- Roleplay: Since you are writing these riddles and challenges, you can control their content, and in such a way you can direct the game to be as violent or peaceful as you want, though in most cases there will be some element of danger when an item is hidden away beyond some challenges.
- Dice: Again, since you are controlling these missions, you can simply decide to play them as a story, and just talk to your players about what they will be doing - hopefully since this method is not part of the mechanics of your system, there will be rarely an occasion to roll any dice - but many players may desire to roll dice to accomplish parts of the riddles and challenges.