Hello!
Now, I made and manage the system like you described. This system include 3 servers with asterisk, 1 server with asterisk+a2billing. Asterisk servers have no web-interface (because I no need it - I manage all via .conf-files and phpMyAdmin), but have cdr-based statistic with call-records. If needs I can install interface for my asterisk in any moment, but me no need it.
Each of asterisk are connected via sip-trunk to a2billing. At a2billing I have some trunks to diferent providers.
Today, this system serve 5 companies. (3 on one of asterisk-server and 2 on other). Admins from this companies have access to a2biling customers interface. They can watch statistic of calls, who made call (name of device or user from asterisk) and simulate call.
All of them installed and configured by me. Without any help from other users. If I will have a client who needs management interface, I wiil setup virtual server with any of interfaces like elastix, freepbx etc..
As you can see, I have some experience in building systems like desired. If you want, we can talk in chat about system witch you need. If you tell me more about desire system, I can tell you how it I see and what I can to do. And after that, you can make you choose.
Best regards, Andrii.
P.S. Yes, I have some ideas about how make system which will manage via web-interface, but I don't can make interface, I can only build all system and say how to built interface. Or how to make system you needs with opensourse programs.