The parking lot at Newspaper Rock is too small to leave your car for the day. Best bet would be to call them and ask if you would need to pay a double entrance fee to park your car at the big parking lot at the visitor's center. Their phone number is 435-719-2313. You can also contact them by email
I wouldn't personally have any issue with leaving my own car on 211 near the intersection where you turn off from 191. There is plenty of space to do so. It would make an easy spot to meet the group, since we usually stop there to let the slower vehicles catch up to the leaders and make sure no one misses the turn.
We usually depart at 7:00 a.m. sharp from the south end of Moab. You can calculate the mileage to the intersection of 211 and figure how long it will take you to get there at 50 mph.