Build me a better WebRTC video chat page

I am a retired software engineer and I have been tasked by a non-profit organization for the elderly to implement a very simple app so that at the touch of a button two elderly people can communicate from any web-enabled device (and any browser) and avoid the complexity of current mainstream apps which most elderly can’t manage. I can do all the rest myself, but we need a better video-chat HTML/PHP/Javascript page/module to which to pass three parameters (two nicks/usernames and a role, as for example “Alice, Bob, Initiator" (or "Alice, Bob, Responder") such that a peer-to-peer webRTC remote communication is established. This communication could be established via what is called in WebRTC jargon "server-less" (via a STUN server service you recommend other than Google’s free “test” STUN servers) or our own (yes, we can setup our own STUN server but maybe you suggest a professional, industrial quality one to which we do not need to do IT maintenance). Signalling is to be done by passing/conveying SDP offer/answer messages between Initiator and Responder via MySQL database (see example) or else POST/Form or maybe some other method (WebSocket?). We can discuss any other solution/architecture you deem appropriate. Our most important requirement is that 99% of communications are established “phone call like” within 20-30 seconds or less (with no--or very few--"ICE Failures”—ICE as in "Interactive Connectivity Establishment” protocol). The code you supply will be license-free as in we will own all rights and copy rights to this module not to be exposed or expose the users to unexpected debts or charges. Communication and connection must be smooth, seamless, quick and easy between any of the main browsers both either between mobiles, tablets or PCs. The attached example (with SDP message conveyance via MySql DB polling) works and complies (mostly) as described but has too many iceConnectionState of “failed” which is frustrating and confusing to the elderly: we need one that is more reliable and has a much, much higher communication “completed” iceConnectionState rate (of about 99%). Mind that the example works fast and well--but only 50% of the time—and we need MUCH better (99%). The final product delivered should show two html video elements, a chatbox and a text input box (more or less as in the attached example). Thank you in advance for your help. To run the attached example use: [login to view URL] (in one device) and [login to view URL] (in the other--notice only "Role" differs, and that only the Initiator can start communication).