As a services contractor, I will start by saying there are some pretty good acquisition shops out there. NITAAC at NIH comes to minds. But, we must remember procurement is more than the acquisitions office. It is also the program offices. They need to work closely to run an acquisition from its early stages. Program people must also understand the FAR better than they do. There are many things I could address, but one would be to allow flexibility. If every agency had the ability to look to a NITAAC (call it competition among acquisition offices), which would include all offices being able to charge a fee for the service, I think you would see agencies gravitate to the better ones and the others striving to get better to gain the business.
I would also suggest you not limit your review of private sector procurement to the large companies. Start with the companies who are trying to do business with your agency, whatever the size. You might be surprised what they may have to offer to improve your processes.