I am in the same situation right now, did able to get the license by showing the copies of old NJ Driving license . Please share your experience.
My situation was a bit different. I was in NJ and then moved to Virginia. When I moved to Ontario, I surrendered my valid Virginia license in lieu of Ontario license. I also had to show the certified original copy of the abstract from Virginia DMV and based on my experience they gave me a G license. So bottom line, in order to exchange a US license for a Ontario license, your US license need to be a valid one (non-expired) and also provide a certified mailed copy (not a printout) of the abstract. Copies of old license
and abstracts from previous states only help past experience to be counted in the total experience. For eg. if you have 1 year driving experience in current state and 4 years in previous states and you provide documentation of the previous state then your total experience is 5 years and you get a G licence. However, if you show only the one for present state you may get a G2 because there's a minimum no. of years of experience you need to have in order to get a G. And even if you have the required years of experience in present state for a G license, you would still benefit from the additional experience because insurance companies would give you a rate based on total experience and not only the license category G2 or G.
P.S. The abstract you get for a NJ license as an online service, is useless. It doesn't show your license issue date and other historic data. As someone else suggested in this thread, the correct way to get one is submit a DO-11 form ( you can do it via a friend in US in case you have already moved to Canada)
When you request through a DO-11 form, you will have to submit one for each time you have renewed the license in order for them to provide record of all the past renewals.
For eg. if you got your license for first time in 2018 and it was valid till 2021. Then you renewed in 2021 and it was valid till 2023. While filling
DO-11 form Section C you will see Month Day Year. You may skip month and day and just provide the year you applied for the license (first time or renewal). If you provide 2018, they will only send you the abstract showing your license issue date in 2018 and expiry date as 2021. You will need to submit another DO-11 form and another check of $15, and mention year as 2021 and only then they will provide another record showing license issue date as 2021 and expiry date as 2023