According to the guideline I pasted, you can not separately bill the CC time just cause of a shift change
For Medicare Part B physician services paid under the physician fee schedule, critical care is not a service that is paid on a “shift” basis or a “per day” basis. .......... Physicians assigned to a critical care unit (e.g., hospitalist, intensivist, etc.) may not report critical care for patients based on a “per shift” basis.
Think of it this way. The patient didn't make an ED appt with a specific Doc. The ER Docs are there as an "assigned team" to provide care for the ED patient. The ED Docs are to code/bill as one Doc regardless of who "on the team" has treated the patient. Make sense?
So, combine the CC time into one billable session and for me, I would bill all the CC time under the Doc that ended the session.
You said you had 35 min and then an additional 40 min for a total of 75 min. The CPT 99291 is for the first 60 minutes, so code 99291. That leaves 15 minutes still to bill for. The 99292 is defined as an additonal 30 minutes and you must meet that code 1/2 (or 15 minutes) in order to code it. And you do. So code the 99292 for the left-over 15 minutes
The "1/2 way rule" is why 99291 goes from 30 to 74 minutes. At 74 minutes you are 1 minute short from meeting the 1/2 way rule. So if your total time would have been 30 + 40 for a total of 70, then you would have only been able to code 99291. Make sense?
And you can't code/bill a 99292 without first coding the 99291. The 99292 is an "add-on code" which is why it is marked with the little "+" sign in the code book. And you must have at least 30 minutes of CC time in order to code the 99291
As far as Doc #1 complaining he didn't get any coding (workload/payment) for his time treating the patient....that is a separate issue from correct coding. The ED Docs would need to take that up the chain to be reviewed to see how often this scenario comes up and much it affects each ED Doc. Not your issue