Hello,
I'm not fan of the timer. I never like timers, in any games. I like to look at details, explore, try things... With a timer, i just want to rush and go the the end as quickly as possible, sure it's the goal of a timer, but it wastes content, in my opinion.
Also, i don't like timer linked to health. I'd prefer if i have maybe only 1 hit, upgradable to 2 hits maybe, and after i'm out of hits, then the timer starts and i can remove it with food.
So, i start with no timer, and i can be hit once.
If i don't have hit left, the timer starts, faster than the one we have now (10 seconds ?)
If i eat a fruit, the timer stops, and i have one hit again.
Later i can improve my hits, so i can take 2 hits before the timer starts.
With a dino i can take 3 hits. First hit removes the dino. Second hit remove one hit... Last hit starts the timer.
For boss, there is no food, so i must kill the boss without taking a hit, or within 10 seconds, so it's safer to bring a dino so i can take one hit "safely". Then you love your dino more.