For context, I've tried some apps that make you solve puzzles / maths problems but when I'm tired I just restart my phone and the alarm stops (because they're not particularly well made).
So you're napping to re-energize, not compensate for exhaustion.
That way there's always a subconscious motivation to get back up and into action.
Plus it sure takes less rest to re-energize than it does to recover from exhaustion, which may never happen in one day anyhow.
You may never need an alarm clock that way.
That in itself can be a big ask, in terms of lifestyle issues that might be needed to mitigate exhausting outcomes.
And that might help the most alone on its own.
Or if you still want to benefit by fitting some napping into more of a mainstream productive workflow, the thing to start working on is to fall into a worthwhile state of rest more and more rapidly whenever you would feel the situation appropriately contributes to better productivity.
You don't want deep sleep anyway, just maximum rest in the shortest period of time.
IOW maybe also you're already doing everything right, and just need to reduce the 30 minute wind-down period to only a minute or two. That may not happen overnight either, but can be an achievable goal.
The call of nature is one that cannot easily be ignored.