For eXtended, you want the voltage to exceed 150v by a minimum of 10v, at the lowest operational power line voltage (usually 10% below 120v). Close enough is to add another 10%, for 176v total at 120v power line.
To avoid ringing in the power supply, the best tool is PSU Designer II - freeware downloaded from Duncan Amps. To use it you'll need to know the open-circuit voltage (174v) and the effective resistance of each winding (133 ohms). Then just model the supply - you already know the current draw (20mA). It's a bit of a learning curve but well worth it. The inductance and the resistance of any choke will both play a part, so there's no "optimum" - it's more like a variety of pretty good choices. Hammond 155J is 15 henries, 30mA, and about 1000 ohms, looks like it would suit your purposes. 154G is a bit smaller and might work, too.
In most cases, the 6.3v winding won't make enough voltage to keep a regulator from dropping out of regulation. Just FYI.
