I might not be understanding the methodology as a whole.
If in a week I do 14 +17 dungeons, and then I decide to make a +3 with my best friend who doesn’t have enough ilvl for a +17. Will that mean that I get a +3 ilvl piece of gear to choose from at the end of the week?
From what I’m seeing on Wowhead, it’s guessed to be the lowest of your top 15 runs but it’s just speculation. If that’s accurate, your 15-run option would be based off of the +3 in your example. It should be noted that the different chests are just options; you don’t get all of them.
We know how the first two rewards are determined and can extrapolate this to the 15 Dungeon reward.
The first reward is determined by the highest key you complete this week.
The Complete 5 Mythic Dungeons objective is determined by the 5th highest key for the week.
Here’s how it works. The great vault rewards content based on a % of content that you do. So if you do, as you say 14 keys at one level (17+) and 1 key at a different level (3+) your choice of rewards will all come from the 17+ loot table.
Same with raids. If you do 9 bosses in Mythic, then one boss in LFR, you’ll get mythic raid choices from the great vault, and no LFR pieces.
The reason they’re doing this in particular is to avoid situations that are exactly the opposite of what you’re describing, with one person doing a single M17+ and then filling the rest of the dungeons with M3+ and getting loot that is from M17+ dungeons in the vault.
Sounds like its the lowest, not the last. They should at least average them. Now nobody will be able to help friends out until they complete 5 or 15 runs.