First, don't think of the ride as 64 miles. It's really only as long as the distance between rest stops. You just have to ride more than one.
Second, you need to spend more time on the bike. 15 miles isn't really a long distance considering that your overall ride is 4x longer. You can liken it to your marathon training, 6 mile runs wouldn't cut it. That being said I think you can use your marathon training as a base for your cycling training. Just scale up your distances. A good resource for longer rides is your local cycling club. If you're in the Durham area, I can point you to a number of links. My advice would be to get on your bike everyday even if it means you cycle 2 miles in the morning to get a newspaper. Then try to supplement those rides with longer rides at least twice a week, once during the middle of the week and once during the weekend. Tailor your energy expenditure to match your distance. For shorter rides you may want to go much harder than longer rides. Allow some time for warm-ups and cool-downs.
Third, I think you need to learn to rest on the bike. Find a club ride, grab a cue sheet, and ride with the fastest group you can for as long as you can. When you get dropped, spend the rest of the ride pedaling but recovering your legs. When they feel OK, attack the next hill and see how long you can keep it up. Rest, attack, rest, attack, until you're exhausted, then finish the ride at your recovery speed.
Fourth, you need to think about your equipment. While a number of people will tell you to get a road bike, I think that's an unnecessary expense. I would start by getting road tires for my mountain bike. That alone will decrease the amount of energy you expend. Next, think about cycling clothes. I'm a big fan of having a jersey, simply for the pockets. You can find cheap ones on the web. And for your bottom, you need to think about your saddle/shorts. It's a bit counter-intuitive but a harder seat is better for longer rides. Softer seats tend to move a bit and can lead to chafing. Unfortunately, the harder seats take a bit of getting used to which is why cyclist go for padded shorts. If you're looking to get away cheaply, try padded underwear and wear some sort of compression short over top.
Finally, there's a mental aspect to longer rides that you need to address. The bike can be mind-numbing at times so you need something to help. I used to leave the start of charity rides near the very back. Then I used riders up the road as motivation to keep going. Nowadays I simply ride with friends who are closer to my speed. Either way a distraction is a good thing. Avoid portable music, it can prevent you from hearing oncoming traffic.
As I think of other things I repost, but I think that getting on the bike frequently is the key. Don't expect your fitness to come back all at once. And as you get more fit you may find that your mountain bike doesn't have the gearing you need. Only then would I think about an entry level road bike.