None of the below will solve any problems with M+ playerbase, because as someone mentioned above, you can’t patch player behavior. But I like going on wild brainstorms now and then, so here’s a drizzle:
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Remove the timer and instead balance the end reward based on the number of deaths.
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Remove the key downgrade for finished runs, even if they are at the worst mark. The worst outcome from actually finishing a run should be lack of key upgrade.
3a) When you leave an M+ group that is in an active run, whatever key you have (if any), downgrades by one level. If you’re an elite awesome player, you can just find another group and push it right back up, which is what you’d rather be doing anyway, right? 
3b) Alternatively, upon starting an M+ run, remove everyone’s key from their inventory, and award them a new one at the end of the run (group disbanding also counts as “end of the run”) based on group performance and on the key they had, if any (so going into a +12 run while you own a +5 key, and timing it with one star should get you a +6 rather than a +13).
4a) Allow people to choose the key level they want to run (up to the level they have ofc), and use that as a baseline for end reward. So if I have a +12 key and decide to run a +9 with it, it counts as a +9 run, and timing it with one star should give me a +10 rather than a +13.
4b) Alternatively, allow people to downgrade their keys willingly if they choose to do it. It can sorta already be done by starting a run and then leaving it, but why not streamline the process a bit.
Bananas/10) Alternatively alternatively, and just because I’m feeling a tad vicious today, remove keys entirely and instead let people run any dungeon at any M+ level they qualify for though the dungeon finder tool - so you’ll always be grouped with people who chose the same level. Let people queue up for up to three or so different dungeons/key levels at the same time. Downgrade levels of qualification by 1 per week of inactivity. Premade groups can still be made by those who want to be more particular about who they take.
None of the above will solve any problems with M+ playerbase, because as someone mentioned above, you can’t patch player behavior.