Instead of simply speeding up the player, why not simulate reality where, when a serious adrenaline surge hits, everything seems sharper and slowed down? I don't know if you can add a 'desaturate' or 'high-contrast' shader or not, but slowing everything down is entirely doable. As a side benefit, it gives players more time to think about what they need to do and then do it, thus making the game more enjoyable. (I use the 'Speed Control' mod to drop the game speed to half when attacking biters as my twitch skills are long gone.) I would also ramp the speed decrease depending both on the player's hp loss and the number (and difficulty) of enemies nearby.

Does that make sense?

a 'desaturate' or 'high-contrast' shader

Mmm, can I?.. (I have a one sillish idea for 'desaturate' actually... it's interesting) (it doesn't work. However, if I'll use sprites, then I can create effects like fogs etc... OR I have to do the weirdest things with data. I found "camera-effect" with "screen-burn" but I don't see how it actually works...)

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but slowing everything down is entirely doable

It's quite safe for singleplayer sessions but for some multiplayer sessions it'll be more... weird if it's a PvP game or all players will be slow, but only ~10% of them are fighting... (Shortly, it'll work more complex for multiplayer sessions)

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on the number (and difficulty) of enemies nearby

It'll slow game performance although if the game will be slower...

You might think that the game slowing down for other players might be a negative, but it worked VERY well for Killing Floor. As long as players understand that when it slows down it means that someone is under attack and NEEDS that extra time to react, I'm quite sure that most will be fine with it. Personally, I would make it a default setting that can be changed. (I quite often drop the speed to half while I'm figuring something out and then forget that I had left it there until I start moving more than a short distance. In practice, it really isn't a big deal.)

In short, it fits so perfect for some effects or as a game mechanic (for example: "SUPERHOT")

Killing Floor has/had moments like everything is slow but no enemies near some players sometimes.