Call me crazy, but I'm going to tell you how to do much of what our tool does using just 3CX.
Essentially you can assign to a queue both the agents 3CX extension and a dummy extension (one assigned for each agent) that forwards queue calls to their cell phone (Unfortunately, you cannot enforce who is logged into the queue).
If nobody answers the queue call within the max wait time, forward the call to a voicemail box that emails to a distribution group.
How we add value --
First, let's address the schedule of who is on call and when.
Our tool provides an easy to use web calendar to set up recurring schedules. For example, I could be on-call every 3rd week on Mondays, Wednesdays and Fridays if you like. You can get pretty creative with the schedules. Then, based on the schedule, we ensure the right people are automatically logged into the queue at the appointed times. Further, you can have different schedules for different groups. No point notifying "everyone" if the call is for a specific group.
No more questions about who was supposed to be on call. No more updating forwarding rules or passing around the on-call cell phone. Just set up the schedule and forget about it.
For a "live answer" option, you could rely on staff to remember to keep their 3CX Phone client active and logged into the queue (forget ring groups), but you are already having problems with that...
OK, nobody answered the queue call. What do you do then?
Let me ask a question. If nobody answers the call in the queue, and the call fails over to a voicemail box, is a beep that you received a new email sufficient to wake you up at 2:00 a.m. in the morning? Our tool will call you on the phone, send an email, and send a text message and wait.... if nobody answers the voicemail in the allotted time, it will notify them again, and again, and again. If they still do not listen to the voicemail, when we can add more people to the list of people being notified (up to 30 levels of escalation with multiple people in each level).
What about logging? Can we know who was notified, and when?
We log everything -- when the call came in and from whom, who was notified, and how they were successfully notified (phone, email, SMS). You will be able to see a chronological history of everything that happened including when the voicemail was heard. You can even add notes to the log so you know the resolution.
The logging function removes any question about who was or was not notified and when. It is a great tool for monitoring your SLAs and who is actually taking the after-hours calls vs those that let it escalate to someone else because they do not want to get out of bed.
No more excuses about "I didn't get a call". You know who was called and whether the notification was successful. And you don't have to rely solely on one channel of notification. At 2:00 a.m. the more channels of notification the better.
I guess you have to weigh the cost of our tools against the cost of losing a customer because you didn't get the needed notifications.