An alternative to a wired dongle is a high-quality bluetooth amp, e.g. from Fiio. It's reliable, keeps your phone free from cables, but you can keep using your high quality wired headphones.

That seems a ~~wired~~ weird compromise to me: you get the downsides of Bluetooth (inherent latency, potential codec quality loss, spectrum congestion — I occasionally experience interference and dropouts in crowded areas) but still have a wire hanging from your head and another battery to keep charged. :/