Its a good question, and the very best way you can measure hours spent on a development project is not to measure hours spent at all.
You say there is good will to register hours, but I have my doubts. Realistically, from a developers point of view, excessive time management is a distraction for most (perhaps ALL developers on the planet).
I can understand why time is measured so excessively on ODesk. There is a good reason for this, because project time is paid up front by the client to ODesk, and the developer needs to prove to ODesk hours worked. Payment is also guaranteed, and its unlikely oDesk providers and developers ever meet in real life, so there is no trust.
Since its unlikely you're paying your developers upfront, and its more likely you have better trust established, you need to perhaps switch your attention from a management strategy that's cludgy and annoying, to something way more useful.
Yes ladies and gentleman I am talking about Scrum. Throw any notion of keeping hour per hour tabs of your developers out the window (they'll love you for it). And instead introduce Scrum Management into the scenario.
Create some sprints (milestones) for your product development, and in that have a list of iterations (batched deliverable s), try keep your iterations down to a weekly period.
Create a product backlog, and make sure you're aware who exactly is working on what. Find someone on the team to act as a scrum master on your behalf, or to take on this responsibility yourself. Make sure you have daily feedback meetings, keep them short and focused, to identify any risks that might get in the way of deliverable s. Let the developers more or less drive the timing process, and get realistic estimates for tasks.
Read a book or 2 on scrum, and get others and team members involved in the learning curve. Tweak the base scrum methodology to best suit your particular style of management, and I assure you, you will have a very happy team.
Measure your time in man days, and try avoid getting on the back of a developer for hour by hour progress...