By "altering gameplay" i mean without causing games to drag on forever or creating overtly adverse effects that fundamentally cannot be rebalanced even with changes to other systems because they are inherently broken.
So here is a suggestion that is tame enough that it doesn't have overtly adverse side effects:
Assists reduce your death timer by 20%
In other words if your team gets aced and didn't manage to kill anything more than a couple of people on the enemy team, you are still going to lose towers, objectives, inhibitors and maybe the nexus depending on circumstances.
But if both teams manage to trade roughly even, most of the people involved don't have to sit on their hands for half a minute to a minute.
Furthermore, watching your death timer go down in big chunks because of that big awesome sacrificial play you made happen makes you feel good; and lets be honest, some champions playstyle is just kind of suicidal by nature (looking at you diana)