Seems like you should be able to whip up something for yourself then.
Planscope is way more of a project management tool than Freshbooks (as it's primarily invoicing), so it would be worth giving planscope a try for a project.
2. Ledger for CLI badasses.
3. Org-mode because time series data is essentially lists with time stamps.
4. Paper and pencil, because if that doesn'twork, then the issue is not technology. It's habit. Personally, I'd go with paper and pencil to develop a workflow before fooling around with technology.
But, the problem with going over budget boils down to one of two things: poor estimates or buying the job.
Lastly, if you're billing hours internally against a fixed price externally, there's always going to be an impedance mismatch. I know that HN'ers love to promote fixed price, but if it doesn't work then don't use it: bill time and materials instead.
Good luck.