I would like to get a cloud service with native integration to GP for AP automation, PO approvals (including inventory items) and a dynamic expense system that integrates with our company credit card. Am I asking for too much, or does anyone know of a solution that will do all of this? My dream is to move the PO process to the cloud with it writing back to GP, so when we move to a new system, the PO process does not change for creators or approvers.
There are many options out there with a variety of integration/functionality options. Most common integration method is via GP’s eConnect toolset.
There are too many to name so I’ll just mention the most common ones our GP clients use for one or more of the processes you mentioned that (I believe) all integrate with some version of eConnect: Mekorma, PaperSave, Gorilla Expense.
All of these are generic good-for-most industries but there are a whole bunch of others that are industry-specific.
There are also many with more manual integration but are common cloud products (like Bill.com that abandoned their eConnect connector 
).