Grow Schedule for Best Yield?

I’m thinking of planting on May 1 (New Jersey, USA) under daylight and just let plants take their course until flowering naturally. 12/12 doesn’t happen until late Sept, although days become shorter after June 21.

Is this too long for the veg cycle? Does a grow period from May to October cause problems of any type?

It should be fine. You can veg for quite some time.
Your plants will get very big or just big so you mite want to keep
an eye on them. You can tie them back and when the lord switch’s to 12/12
you’ll be just fine