IMO, push buttons rule, here. Just fix your resolution.
You don't need 99 hours. And you don't need 29 seconds.
Button 1 :ADD 10 minutes per press
Button 2 :ADD 5 minute per press
Button 3: ADD 1 minute per press
Button 4: clear and turn off timer
Timer starts automatically, after the first button is pressed.
Each press increments, only. If you go too far, clear and start over. Takes a few seconds, and is very intuitive. If you're gonna cook a turkey, pressing a button 9 or 10 times is not too bad, really. It's the thinking that sucks. Watching the numbers go up when you hit a button, is very much not like thinking and is much more like doing. Setting an 80's alarm clock sucks. It's not just about how long it takes to set. It's also important to minimize how much attention/learned skill/dedicated memory it requires.
Plus when you go check and it looks like it is going to need another minute or two.. just press the button. Don't have to stop and recalculate, subtracting the time it takes you to set your 80's alarm clock. This gives you much more ability to undershoot if in question, and modify later, if/when needed. Cuz no one knows down to the second how long anything will take to cook, unless they cook dinner with lab scales and thermometers.
Just make the debouncing invisibly fast and use a nice tactile button.
Personally, cap/slider annoys me. Esp with acceleration. They are cool to whoever wrote it to work just as they want it. But they are biased. IMO, not too many people want a cap/slider interface for a kitchen timer. That's a solution looking for a problem. There's no way you would ever swipe a surface and trust you got it right, without looking. Pressing a button, you can do that with your eyes closed. They are best left for very tiny devices for cost and longevity reasons, where custom molded buttons will be expensive and or can crap out. Esp for things where you get instant feedback... e.g. volume control.