The best quality you could get would be a G.711 VOIP service with a good internet connection and a voip converter box. Skype business offers it, I don't know about oomu or whatever all those other voip providers offer anymore.
G.711 is the old encoding the phone company has been using for years. You might need to pay for premium service for it though because they would rather you use one of the new high-compression (sounds terrible) ones. Whatever AT&T is giving you over uverse is probably this anyway though.
https://www.dialgizmo.com/ Seems to catch your pulse dialing and convert it to dtmf.
Have you tried a POTS clec?
