We use Harvest to track our time, which has an API (http://www.getharvest.com/api).
We use Staction for updates and todo's, which also has an API (http://api.staction.com/documentation/)
In staction you can enter time in your entry. For each Staction time entry we would like to have a connector that will create a time entry in Harvest.
Each entry would need to grab the following from Staction and add it to the Harvest Entry
time spent on task
user that entered time
project the time is billed to
the note for harvest should be the entry in staction
We can work with you to define a default task in harvest.
You would then need to deploy as a cron or scheduled task on the rackspace server cloud environment.
I'm thinking there would need to be an interface that, as we add new projects or people, we would need to associate the Staction entry with the Harvest entry (I've attached a pdf of how this might work)
I have no idea of the budget, so ignore what I put in and budget based on what you think it will take to complete.