From what I know of them, it sounds as if you are getting it right as the instructions recommend letting the roots fill the pot before potting on.
Re the leaves browning. - Anthuriums grow best with day temperatures of 78 to 90 F, and night temperatures of 70 to 75 F. Temperatures above 90 F may cause foliar burning, faded flower color, and reduced flower life. Night temperatures between 40 to 50 F can result in slow growth and yellowing of lower leaves.
I suspect once you repot all will be well, dont forget to feed and provide good drainage.

Humidity is also important. Unless your heating system has an exceptionally good humidifier attached, I would keep a tray of water under the plant, with the pot propped up ABOVE the water level, on stones or pot feet, to provide a cloud of humidity.

Thanks for the reply, any advise is much appreicated.