Do you think a version of Quinn's old ult could exist in the game while being healthy and balanced? ‘Marksman who turns into a melee assassin’ was such a cool and fun aspect of her gameplay; I’ve never understood the argument that it’s an inherently impossible design to make healthy.

You're not going to like this answer. I don't think that "ranged dps that turns into melee dps" is ever an ability we can support. Abilities exist in a context. Different patterns need very different contexts. For instance, range dps need to be VERY careful how much defensive stuff they get; melee dps cannot live without defensive tricks. The primary skill check for ranged DPS is soft commitment: how close to a fight can I step without having someone dangerous jump on me and kill me? Conversely, melee dps have to judge timing, resource usage, angle of approach, and their defensive tools to decide when to 100% commit to a fight. That means you'd need to have two completely different kits to make this work: one ranged with the usual ranged skill checks (skill shots, traps etc) and only soft defensive tools, and one melee with pretty heavy conditional damage amp and powerful defensive tricks. This is all very abstract. Let's look at two kits and compare. Let's use two popular champions: Yasuo and Jhin. Jhin has a perfect kit for a ranged champion. His defense is highly conditional: not only is his W dodgeable, it requires a mark to root the enemy. His R has a powerful slow but requires him to stand still. He has an incredible damage amp in his fourth shot, but it's highly windowed. He'll hang out at the edge of a fight and hit who he can, opportunistically stepping forward for a 4th shot kill. Yasuo has very powerful on demand damage that becomes massively more reliable at close range (due to EQ). His damage has pretty much constant uptime, but requires him to chain Es and use Windwall at just the right time in the right place to be able to live. Once he fully commits with R, he either starts killing everyone or dies. There's literally no meaningful overlap. Jhin must have poking/fishing skills on low cooldowns to function; Yasuo can't have them without putting himself into risk or his damage would have to be lowered to where he wouldn't function. Yasuo has a game-altering defensive window that's HIGHLY conditional and windowed, giving him the time he needs to be a melee threat, while Jhin cannot have ANYTHING that sharp defensively. Everything from itemization to stats to tools on the kit must be built around a champion's engagement pattern; you can't just switch patterns and not expect one of the two to be broken with the tools that belong to the other pattern.