Forming a non-profit at this point will require a registration for a new enterprise, with a board of directors, a charter and an IRS application approval for tax free status such as a 501 3(c). My average non-profit client spends 6 months achieving these matters. You should also know that you do not own a non-profit. Your community owns it and as the founder you will be working at the behest of the board of directors.
There are industry teaming and direct contracting opportunities available to you in your current status as a business. This is particularly true withing the VA and withing many of the armed services hospitals.
The following article contains additional information you may be able to use and compares the two entities you are considering.