My company also uses single entry mode. Here’s how we configured it to accomplish very similar results.
There are two approvals. First being approval of the timesheet itself and second being approval of the status update into the project schedule.
For the first approval (timesheet itself), we made each person their own timesheet approver. That way, when the timesheet is submitted, they automatically approve their own timesheet. After clicking turn in final, the timesheet automatically updates and shows that XX hours have been approved by [their own name]. So this gets us past the initial timesheet approval step.
For the second approval, we have the PMs establish automatic approval rules in their approval center. Unfortunately each PM needs to set up their own approval rule, but the rule is pretty simple. Approval all status updates for all current and future resources and all current and future projects. We don’t however allow auto approval of anything other than status updates. Meaning, remove tasks, add tasks, etc. still require PM approval.
So, the net result of how we have timesheets setup with self approval and auto approval rules is that the timesheet is submitted by the team member and automatically applied to the schedule with no other intervention.
Regarding the Timesheet Send button. I don’t believe the Timesheet Send button can or should be grayed out. If you do this, the timesheet is always in an open status and will never process against the schedule. The Send Turn in Final function (or any send function) is what causes the timesheet hours to be processed against the project schedule. So if resources can’t click on that button, the net effect is that no time would ever get reported to the schedule.
Also note that timesheets are applied to the schedule immediately, as long as the schedule is not currently checked out. So if the PM does not have the schedule checked out, the submitted timesheets will be approved and processed against the schedule pretty quickly. If the PM has the schedule checked out, all timesheets submitted will wait for the schedule to be checked back in. Once checked back in, the submitted timesheets will start processing against the schedule. I only mention this because timesheets submitted with this auto approval process won’t necessarily apply immediately. Depending on schedule availability or the background processing queue volume, it could be immediate or it could take an hour or two. We have approximately 3000 people submitting timesheets every Friday and sometimes the queue takes a while to process them all.
I hope that helps