I have a dedicated outbound sales person who pings their network for referrals every few weeks. Their job is to weed out noise + educate + convert hourly to project based billing
Went into a lot of detail on Reddit a couple years back here
https://www.reddit.com/r/Entrepreneur/comments/ommiww/commen...
I can see how that helps in increasing revenue, but it also makes the work less agile, requires longer negotiations and adds risks. So it's probably not for everyone.
Some others have found a way to bill similar amounts but on short projects billed by the day/week. That sounds preferable to me, but you need to have a skill that produces value in such short projects.
I assume you're a software developer? There's your skill.
I think you're overthinking this. How is it less agile? You have a project, a price and a timeline. Everything between then and the end is on your schedule.
The only "unintuitive" skill you need to hone is assessing value and pricing based on that. But there is endless analysis and analogies out there to help.