My understanding is that you cannot convert to a CPL directly... Rather, you can get an FAA PPL issued, and then have to do the CPL knowledge test and flight test (aka checkride) etc.
There is a possibility that because you already hold an ICAO CPL, you might be able to skip the PPL issue, and just do the checkrides (maybe some training flights?)... But I'm not 100% on that.
I would recommend you contact one of the Flight Standards District Offices (FSDO), preferably the one you are likely to visit to do the actual paperwork, and get the exact requirements.
Flight Standards District Offices (FSDO)
To get a FAA PPL issued, there were some forms that needed to be filled and submitted to FAA, verification applied for from NZCAA separately (form CAA602), then a letter would be issued by FAA (they advise the whole thing will take like 45-90 days)... Once you had the letter you had something like 3-6 months to arrange a meeting at your nominated FSDO.
http://www.faa.gov/licenses_certific..._verification/
note: extra requirement mentioned for NZ
The meeting was nothing much, a brief chat, a browse of my logbook, more paperwork and then after about 30 minutes I walked away with a temporary paper certificate... The shiny plastic card got mailed to New Zealand address about a month later.
Hope this helps...