There's some really good advice on this thread. FWIW, here's my take.

You are living two lives at the same time. It's possible to do it, but you have to sacrifice and avoid traps. You have to acknowledge you will be vulnerable due to tiredness. Your main pitfall is falling into depression, despair and alienation. Here are some very simple techniques I use. It is vital to achieve a good mindset and excellent health.

Master your time and in particular your sleep. Every day sleep at least 8 hours. Don't moonlight if possible. Wake up very early in the morning, 5 or 6am maximum. Go for a walk or a run, then have a very quick healthy and filling breakfast (avoid boxed cereals!) If you have time, work some on your project. Get to work before anybody else, get sort everything you can in the morning as everybody else is drowsy and slow. Exploit that. Master the "wally reflector", perhaps preemptively.

For lunch time, have something very light like a sandwich or salad. Push meetings to the afternoon, if possible. Focus well on people talking to you, don't multitask on meetings. Avoid the water-cooler gang, don't waste your time even at the office, remember you are worn out more than your co-workers. If you need to clear your mind, go to a quiet place and rest. Do the same at lunch, if possible.

After work, avoid the pub and go straight to your project and put as many good hours as you can. If you work at home, get rid of any possible distraction, in particular avoid time sinks like TV, social sites, and chat/im. Hold dinner until you are done.

Drink water all the time, perhaps a glass every hour. Avoid any other soft drinks. Eat healthier, get enough nutrients in particular good proteins (milk, egg whites, soy) to help you recover. Also don't neglect good oils (sunflower, algae/fish.) A healthy lifestyle will help you save money, too.

Stay away as much as possible from coffee because it will give you insomnia and stomach problems while in the long run you end up with a dependency and without the buzz. Avoid alcohol (and soft drugs), its effects will cascade into the week because you are vulnerable. Avoid heavy and unhealthy foods, it will give you indigestion and get you drowsy. Stop eating sugars, candy, chocolate, and soft drinks.

When you are feeling bad at work, visualize your goals. Repeat to yourself often, perhaps in a mirror: "this is just a stepping stone and I'm moving forward to my dream life." Or something along the lines better fitting your situation.

Keep completely to yourself either Saturday or Sunday, zero work. Have a good time.

Now the hardcore tricks. In just 2 weeks you can clean up from the typical western sugar addiction. Hang in there with your cravings. Only when you are completely in control, you can have a little bit of sugar as last-resource remedy to help you get by when you reach very low points of the week. Drink lots of water with it to even out the effects from 15m to 45m. Don't eat or drink anything else. Sugar is a strong stimulant and an occasional shot can help keep discipline, but it works only if you don't have resistance to it. (There are several studies on this subject.)

Another trick is to schedule properly the work that wears you out. Put it all together and finish it as soon as possible, then resume your normal schedule.

And the best trick is to go to bed early on Sunday night, perhaps get your doctor to prescribe your some light sleep inducing pills. Some people swear by herbal remedies, too. When you start the week with the right foot it tends to have a good inertia.

And the top trick, write a log! Even if you write a single line it will help you keep focus and will help you become aware of progress. Write it even on bad days, highlight what went wrong. It takes just a minute.

Even though this is a hard life, if you manage to do it right it will be among the best times of your life. Things will change sooner than you expect.