My best advice would be to cut something out of this trip, and leave more room to enjoy, but that is entirely up to you.
I have seen people drive all the way out to see something, stop ... jump out of the car, take a quick look for 5 minutes, and then jump back in and off ..... just to tick it off the list.
I would leave everything near Alice for future exploring as you will be there anyway, and it will be easy to get out and around from there .....

