This isn't an area I've investigated yet, if I find something I'll let you know. Or if you come up with a list I'd love to hear also - this is an interesting idea. My solutions have tended to be putting some of the bookkeeping off shore - for example, we put our purchasing, Supply Chain and order processing functions in Asia closer to our subcontract manufacturer and Asia customers in a couple of my startups. But I haven't outsourced the bookkeeping much. Good luck.
Do you want to outsource it or automate it, or both. If you want to outsource it call Ragu at Global Upside (408) 219-8203. If you want to automate it take a look at Bill.com. Or perhaps a combination of both.
There are other outsourcing services in addition to Ragu as well who will process your accounting offshore and I can find out ( one company I consulted for used this company) if you want to look at other options. There is a company called Corefino that will take over your entire accounting function and provide "audit ready" financials. They use the Intaact which is an online SaaS accounting platform. I am also learning about a new company called Engine-Room which will provide full admin services including IT and Facilities