Octave/Matlab are "great" but good luck trying to integrate them
   into a production web application

What problems are you facing with Octave? It has, in fact, been integrated into a couple of production web applications I know of:

https://octave.im/

http://octave-online.net/

https://www.rollapp.com/app/octave

I have promised a while ago to improve its Python integration so that Python and Octave can be in the same process (there are lots of advantages to that kind of tight integration instead of relying on parsing output through pipes). Perhaps that could help you?