Recently, I achieved something of a miracle. I got my wizzie his epic 1.0. Unfortunately I didn't have an open inventory slot so my friend got the epic instead of me. ( This is a big deal for me, what does everyone think?
That's not how inventory works. If you do not have inventory slots it will go on cursor. Is your friend a wizard? Did your friend do the final turn in? Congrats, you just multiquested their epic.
The old task system doesn't track characters, whoever hands in the last piece got the reward. That's what multiquest means, it's not paying for anything (though for rare drops selling the turn in of one of the no trade items before the end is a way to make plat). There is no way for items to overflow to other characters. Either something was done wrong and you'll have to do the chain again, or you didn't actually do the final step. Make sure you are doing all the hand-ins and hails, you especially have to do the last turn-ins to actually get the reward. https://www.eqprogression.com/wizard-1-0-epic-quest/
If you still had the items, then yeah you need to do the final turn ins. Doesn't matter who talked first/last, it's not flagged to a character, whoever does the final turn in gets the reward. But depending on what was MQd, you may have left the NPC in a state where they arent ready to accept the other items.