Yes, you can do it on your own. It is "complicated". I think, there are a lot of subtle pushes you need to continue on in to be successful. Hopspitals for one, IMO, do not "want" to give independence to their nursing pool. I doubt those that do subcontract with me via the agency really know I am subcontracting as an independent.
I do not want to discourage you, for I feel that there are those possibilities to drectly contract, I myself have been unable (or in great part unwilling to dedicate the time to be "dedicated to ONE facility) but... yes it can be done.
The key, is finding the decison maker for the contracts at the hospital. Not necessarily, and not most often, Human Resources. When you place your call to find the decision maker for the contract, as for the person who handles Vendor Contracts, keep notes and contact names, and be prepared to be diligent.
I am sure many on this board can offer great advice.
May I please get the name of your agency who handles subcontracts as I am keeping a list.
Let us know how you are doing and please keep in touch.