DIY for connecting a Plantronics headset to a computer

You mean some form of switch box that allows you use the same headset from two outputs? Sounds simple enough if the appropriate connectors are available. The phone headset may well be only mono though and the noise cancelling function is probably done by the electronics in the phone.

I'd tend to go about it the other way - get a high quality headset designed for music use and use that for the phone.

We use a box created by Plantronics to connect their headphones to telephone(PABX), PC and several other audio sources. It's called an EDAIU, no idea if they offer it to the public. It's many things, but it's certainly not HiFi.