We're a industrial-control company whose traditional UI has been standard win32 applications - we've slowing converting our stack over to a web interface but as our UI needs to talk to lots of local devices, we've hit the problems you described.

Our solution has been to basically mandate that the user install either a small embedded device (ie. RPI or equiv) or manually launch a container. These essentially just serve as a local websocket / api router so Chrome connects to some local "device/container" and then that connects to all the local devices.

Although this is a logistical hurdle, its actually simplified other aspects of development since now this device/container has a bit of intelligence and can act as real middleware to simplify what the UI needs to contemplate. Basically MVC-style development using hardware bits as Controller.