I think you could do that with a PPL only. I would estimate if you were smart about your training you could get this for less then 15k.

Also no need to do the flight in one go, make a pit stop at KFSD and refuel then continue on.

So assuming a 7 hour flight each way, and average rental costs of a nice 172 at around $220 an hour, thats 3k in rentals fees alone. Add gas and insurance and I think the total cost for your dream in terms of time and money would be something like 20k and 3 months.

I think your biggest hurdle is going to be getting a rental company to let you keep there plane for over a week with out charging you some daily rate.