Yeah I've got a ton of recommendations for Hours by other people. Problem is that it's a very basic time tracker. Plus you said you're paid by the day. What if I'm working with contractors by the hour? I gotta know they're working their required hours.
Nice article! And I totally agree with the free users eating up support point. I was briefly part of the support team of another startup and I know it as a fact that there is nothing more agonizing than to see you falling short of time to support your paid clients. The thing is you can't give low priority to free users support requests since then they'll rant about your tool on social media and that's negative publicity for you.
In my opinion, I think no free plan should offer any support.