Its funny assumption that the USCIS would not know if you are out of country since "there is a entry stamp in passport to US but not the exit one".

I beleive there are few nepalese who are as lucky as you are who get DV and Canada PR. And how come you have reentry permit for July 11? My understanding is a green card holder can entry any time to USA. You need a valid passport and Green Card, not a visa. Your question and timeline for some reason does not make a sense.

And last piece of suggestion-try to be legal whether in USA or CANADA so that you dont loose both in greed.