Integration would be way simpler and integrate with different processes if you just entered the Sherweb invoice as a bill in the QB system.

Would need to map sherweb parts to QB products.
The invoice would need to be entered as the last day of the month in QB.
Each line would need 'billable' checked off, and the customer field filled in as per a mapping.

Then we get our AP entered 100% correct, and the items are sitting in a queue to be billed to the client.

This method allows us to easily modify anything in the process (just edit the bill in the system after it is pushed over).

This should be much easier to program in than the current integration. And I don't think you should replace the current - just add to it (option)