Towed - we asked CM and he said there is a lot somewhere close by. Remember, this is the only hotel on MK property, so they are very strict with parking enforcement here. It doesn't always happen, but it happens enough. We've stayed at Contemporary several times, as well as eaten at CM's a ton of times, so we've been in and out of this parking lot enough times to see cars being towed. Can't remember where the lot is though, sorry.
Transportation - Depends where you are staying. If you are staying at a monorail resort, then you could hop on monorail, and get to CM. Of course, it depends upon what time MK opens at, as that is how they determine monorail schedule. If another resort, then again, you need to find out when park opens, and then usually WDW transportation starts running about 1 hour before. Not sure about a taxi as we always have a car (either our own or rental).
Sorry I can't be of more help, as I am sick today, so not that quick with information. I see by your ticker that you are going in a few days, so check park hours and that should help you determine what time you can get over there at. Your ressie is pretty early, so you are going to need to be up and out of the door by way early to make it at least 10 mins before your 7:20 ADR. Be prepared for a long wait at CM just to check in, so you should arrive there by at least 7:00 am.
Good luck, Tiger