Sorry to hear about the problems you've experienced with your Pack. That's a very unfortunate thing to happen at the start of your trip. There seems to be a trend over the last few years with luggage manufacturers using lighter polyester materials rather than more durable (but heavier) materials such as Cordura, and IMHO the newer products don't stand up as well. My favourite Backpack uses 1000 denier Cordura Nylon, and it's lasted through a lot of hard use.
I agree with Frank that the best bet might be to find a shoemaker or other luggage repair place at your first destination. The staff at your hotel should be able to recommend a suitable firm. You'll probably find that the type of sewing kits you'll find at airport shops, etc. are designed for clothing and fabrics and NOT luggage, so any repairs you handle on your own may not last for the duration of the trip.
When you return from your trip, you might have a look at THIS product for use on future trips, which is somewhat similar to the Classic Back Door Bag and also has backpack straps. The manufacturer and factory showroom are located in Seattle and they will be able to explain the features and you'll probably find that this product will last for a lifetime of travel. They also have a slightly larger product (also with backpack straps) if you need more capacity.
Hope you have a wonderful trip, despite this unfortunate problem.