Welcome.
I've always did some type of gym throughout my life but not much of cycling (but for a ride now and then). Hubby is a bike nut too so I got into it for fun.
It helped me lose 12 pounds over a year (probably your size too) and I feel better. Still would like another 10-12 pounds by next summer and I'd be ok. At 52 I'm not asking much more. 
400 miles is a lot of cycling depending on how many days it will be. The most I did in one day is 115km and it is plenty. Not being a "summer" type person, I hate too much heat. I perform better in cooler weather but it is what it is and we need to ride when we can.
Good luck in this very nice project. With a good training program you can do it. It won't be easy but doable.
It would be good if you could find someone that could build you a training program like my physiotherapist/kinesiologis does for me. It helps me reach the goals I have. Cycling is a whole and you need just as much cardio as you need to build muscles to help you push those hills/distances.
Have fun!
Helene
Riding a 2014 Specialized Amira LS4 Expert - aka The Zebra!
2015 Specialized Crux e5 - aka Bora Bora bike