What would be the process to approve a minimal, standardized flight recorder for commercial balloons?
As Ron mentioned, if you want to produce a "standardized" voice recorder for balloons you'd be complying with FAA Technical Standard Order (TSO) C123 (currently revision C).

Along the same lines if you wanted to make a "standardized" flight data recorder it would need to comply with TSO C124 (and you would have to figure out what data would be useful to record, and how to get that data to the recorder). 

If we're not sticking with an established actual standard then the next best thing are the personal portable electronic devices used in the flight - particularly if the balloon operators are using something like Foreflight, Garmin Pilot, WingX, etc. on a tablet. The NTSB lab has a good amount of experience in recovering useful data from these devices, and they can be almost as useful as an actual flight data recorder. Combined with an onboard camera (say a GoPro) capturing audio/video of the flight you can make an excellent reconstruction of events (and since many balloon operators offer their customers a flight video there's a good chance the cameras are already installed...)



It's worth noting however that none of these devices improves the safety of a given flight: CVRs, FDRs and even cockpit video are forensic tools used after a crash or incident to help us understand what happened, but their value is after an incident, and thus usually after loss of life.  

The other NTSB recommendations (including carrying transponders) are aimed at actively improving the safety of individual flights, and may prevent incidents.