You can't leave a rabbit alone for a week. 48h is the maximum you can push it, leaving a ton of hay and of vegetables. I generally don't leave the bunnies alone for over 36h. NEVER give a lot of pellets at once, with hay that will be old news after half a day - your rabbit will scarf down the pellets, eat few hay, which is a sure recipe for stasis, and he will be dead before you get home. Watching him get sick over the webcam certainly won't help either of you. You need to find a petsitter who will come to your home to clean up, give hay, water, pellets and vegetables twice a day. That's what I do - I weight, cut and wash the vegetables that I put in small container in the fridge, and someone comes to give pellets, water and hay in the morning and vegetables and hay in the early evening. Look up the ads on the Internet in your area, search for specialized websites about petsitting or even just normal classified ads websites and ask around, many people will offer that kind of service for around 5$ a day nowadays. I always meet with them beforehand to assess their character and show them where everything is. I ask for a copy of their ID if the website I got their contact from doesn't keep records of their members. Don't forget to leave written instructions, an email where they can join you, and the complete contact details of your vet. I also always leave the first pellet bowl prepared in a place where the rabbits can't reach it, because most petsitters will have a tendancy to give way too much if they are not rabbit owners themselves.
Begin looking now. If you don't find anyone, you can't leave, it's as simple as that.