@John D. the cost of removal is going to be very location specific, seeing that you are in PA and the property is in NJ I would assume it is something you are not going to tackle yourself, even though you are posting in the DIY forum. If I was doing the work myself in my area you can get a dumpster for concrete waste for $250-$300 and rent a Bobcat or mini excavator for a weekend for $500-$1000. but that is only for the removal.
your best option would be to contact a few concrete and request pricing for the new work with removal included. as for pricing it is also very location specific and I cant help you with guessing on that. But you are also correct to assume that this project gets more difficult as the weather gets colder, if you can put it off till spring do that. But if it need to addressed now they concrete companies do have additives that can be added to the concrete for working in colder weather, I don't know much about it because I have not needed to use it before but I do know it is an option.
As for the option of just removing it and planting grass, if I was in your shoes I would stay away from this option for a few reasons. First if your current tenants are accustom to having this space for parking, this could be a negative in their opinion and they could decide not to renew when that time comes. Second thing to consider is if you plant grass in this area its that much more green space you will need to account for during the summer months possible increasing your lawn maintenance costs.