Enable the user to schedule time entry submission to Team Connector. E.g. weekly on Wednesdays 1:00PM, or every X hours instead of needing to click the Submit Time Entries button and choose a time frame.
It would be ideal if it would submit all changed entries (even if entries that are outside the window of time since the last submission) but if it would submit all the entries in the time window since the last submit that would at least be predictable. Best of all would be to submit entries as they are created/modified!
If none of this is possible, adding "this week," "last week," "displayed week," etc. buttons to the Submit Time Entries > Submit Timesheet screen would at least speed up the submit process.