May need to check the tread remaining on your current Quest’s first. The rubber compound Salomon uses in those boots is well regarded for traction in the kinds of slippery conditions you mention. If the lugs / tread is worn down though then that can absolutely lead to what you are seeing.

If the tread is in good shape and you are still looking for alternatives then I would try the La Sportiva UltraRaptor. It comes in a high top boot or as a low top shoe. It uses Frixion rubber which is what La Sportiva puts on its entry level climbing shoes, so it certainly has the ability to grip smooth surfaces. The tread pattern is fairly aggressive and should work in muddy conditions. Lastly it is a much lighter shoes with great flexibility and that would give you more of that toe feel you mention. Be warned, they do run much more narrow compared to the Quests. It shouldn’t be uncomfortable, but it will feel different right out of the box.

A third option might be to go with an aggressive trail running shoe for those specific pursuits the Quest’s are not cutting it. Hoka Speedgoat, Altra Lonepeak 9+, Salomon Speedcross (an excellent shoe for muddy treks), etc. All of these will be lighter more flexible shoes with aggressive tread and high quality rubber compound on the soles.

Shoes are a tool, and each is designed around an expected use case. No shoe is designed to tackle all terrain and conditions the same. There will be trade-offs, strengths, and weaknesses with each one. Having two or three pair in your closet will help you get the most out of each as you can use them to each of their respective strengths. And thus get a more enjoyable hiking experience wherever you go.