fabolos, what exactly do you mean by part-time independant contracting...
Do you have an independant contractor relationship with your client? If so is it,
1) W2 with an hourly pay? In this case they would send you paystubs like their regular employees.
2) 1099? They will not provide you regular paystubs like for regular employees.
3) Your own company where you bill your client periodically based on a contract?
The safest option is to get a regular job with a W2 and a yearly salary. This way you can demonstrate as closely as possible that your current job is same/similar as that stated in your I140 application. A W2 with hourly pay also will work because you will get regular paystubs which will be important if you ever get an RFE for that. It would be interesting to see what others\' opinions on this are. My 2 cents.