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I know this post is mostly not about billing strategy (though that's what the thread is now about), but I'm going to chime in with a simple bit of advice for tech workers that I believe is universally applicable:
Bill days, minimum.
A lot of the pathologies involved in metered billing, time tracking, and perverse incentives vanish when you bill days instead of hours. People have all sorts of weird excuses to talk themselves out of billing days --- "what if I only have an hour worth of work to do?" Bill a day. See how easy it is?
The last consulting company I built had a minimum billing increment of a fiscal quarter. I co-ran a consulting company for almost 10 years that did minimum-daily billing, for a pretty big and diverse set of clients, and nobody pushed back on the billable day. Bill days (minimum), not hours!