The issue is that I have no time to work on it.
I have a demanding job with weekday average hours of 9am to 11pm and often to 1-2am. The workload is constant during those hours with no downtime.
I also work c. 5-6 hours on the weekend. The rest of the time is dedicated to "normal" activities, like housework, food shopping, some exercise etc.
I consume no social media and watch no TV. I get my news on a 10 min RSS scan.
I could reduce my sleep, but I find less than six hours affects my performance / health.
Unpaid leave / sabbatical is an option, but it would impact my financial situation and I need the salary.
I've progressed the idea a bit, but I need more time without interruptions.
I feel like I'm stuck. While my job is rewarding and well-paid, it doesn't allow time to pursue this idea.
Looking for advice from those that succeeded on a project in a similar situation.
There are exceptions. Generally, they require adequate capitalization (financial, social, and/or free-time).
The other test is ideas are cheap and execution expensive, so good ideas are only those that you are actually executing.
The relevance here is that you asked a question here rather than working on the idea (no criticism). It suggests the idea is not as good as you wish it was.
The only way to get work done is to get work done, and the reward for work is more work. Good luck.