First of all, DO NOT USE QUIKCRETE FOR A DRIVEWAY. That is prolly the worst thing you can do. Second, there are curb cutting company's out there but that wont solve the issueon the approach. Next I can tear both the curb and approach out and repour it all as one nice slope to the street and eliminate the big hump from the curb and still leave a edge on the curb box for the water to run against and continue down the road to the drains. Also you will most def need a permit and they will have to inspect it without a doubt. That goes for any city on any approach. I have pm'ed you so just let me know what you are wanting to do once you find out the info I pm'ed you.
Thanks.