It's clearly stated that the US military is still going to be the primary source for the data.
Why not have an open RFP that anyone is able to provide a proposal and if the a existing agency doesn't win, make it independently run?
Logically, NORAD Air Defense Sector controllers have the radar data to provide traffic advisories to civilian airliners flying outside FAA radar coverage, but they rarely do so. If an unknown aircraft is detected above 18,000ft (i.e possible collision hazard to airline traffic) without a transponder and within the US Air Defense Identification Zone, ADS controllers may attempt contact on emergency guard frequency 121.5, which is commonly monitored by airliners. There are also USAF/USN controllers responsible for specific sectors that may attempt contact. ADS would likely scramble jet fighters too.
How would an RFP work? How are agencies like FAA or NASA or the US Forest Service supposed to bid on this if they don't know they'll have the budget for it?
Congress would review the proposals and select the winner and provide the budget needed.
Honestly at this point, strongly feel there needs to be a agency explicitly responsible for commercializing space - and neither FAA or NASA have a track record of doing this.