I run a business that works to provide electronic goods to our customers, and we have serious problems with customers defrauding us by claiming failure of delivery or similar through our current processor, paypal.
As such paypal is shutting down our account due to an excessive number of reversed charges from our customers, and we need to find a new provider. I have contacted amazon payments and google checkout but they won't work with our fraud rate.
What options do I have for payment providers for companies that work in high fraud industries?
You might consider trying to solve the problem by moving the risk of loss to another company. That might sound odd, but that is the extra small fee you can pay to ensure the shipper has a valid acknowledgment of delivery, or you get your money from them (insurance).
Since your question is about payment processors, go back to PayPal and everyone else you might want to work with and ask them if using a acknowledged delivery service will help you improve your score. It should. Talk to their risk prevention department and let them know you are interested in reducing the fraud so you can both do better working together.
Depending on location, start by looking at the big shippers, FedEx, UPS, DHL and national postal services. That will give you a baseline of cost if you want to compare further (I prefer to use one of the big ones if at all possible).
Shipping insurance for start-ups is often a great way to distribute your risk across sales, at least until revenue is sufficient to consider self-insuring for the risk of fraud loss. Generally when costing transportation for goods I will "bake in" the cost of insurance. If I can't afford it, I consider my margin too lean for a start-up. I then focus on the margin as the primary problem.
Your situation seems similar to what a lot of file hosting websites are facing right now. Many of them are getting their paypal accounts banned for being high risk. You can find a bunch of payment solutions that people are using for high risk payments here: http://sibsoft.net/forum/need-new-payment-methods-t4338.html
Before you do anything, make sure you don't have a technical issue. If you really have this high rate of fraud-reports against you, then it's highly likely that those people really weren't able to download or receive their content.
Sometimes it breaks down to something as simple as a misplaced button or a button that doesn't work on some browsers.
Double-check and make sure that your buying-process works flawlessly on all browsers and from inside and outside of your office.