My thought on this is to start from the question of whether you can land on a taxiway at an airport without a control tower, on the theory that taxiways are more regulated than the grass margins of the runway beyond the runway lights. My logic is this: If there is a rule about landing on taxiways, it will either say "areas other than runways" or "taxiways" and you'll know if the grass is covered or not. If there is no rule against landing on taxiways, then we have to dig deeper to see if there is a rule against landing on the grass but it seems unlikely that they would prohibit landing on grass areas but fail to say anything about taxiways.
Here's a thread elsewhere discussing the taxiway landing question:
https://forums.jetcareers.com/threads/legal-to-land-on-taxiway.77334/ There is a link to an approach plate with a supposedly interesting and relevant note, but unfortunately the link is broken. Searching for the filename brings up a 2013 version of the plate for GPS RWY 31 at KMWL, but the but the thread is from 2008 and the note appears to have disappeared in the intervening 5 years. The thread does conclude that there is no federal regulation other than 91.13 that says anything about where you land other than at airports with operating control towers.
Another thought is this: Helicopters don't have to land on the runway. What makes an airplane different from a helicopter? You might think that "airplanes need a runway to land and helicopters can't taxi very well because of those skids" is a good answer to that question, but all you end up with is a continuum with helicopters on skids on one end and airliners on the other end, and a plane with a tailskid somewhere in between them. With a tailskid, I think it's arguably more careful to land in the grass next to the runway than on the paved surface, not just for you but also for other aircraft since you are not going to simply pivot and taxi off of the runway.
You will need to be cautious about state and local rules. I don't know if the courts have addressed whether the FAA's regulation of airports preempts all local regulation about where on an airport you can land an airplane but, if nobody has litigated that issue already, I do know that a new tailskid costs less than the legal fees to go to federal court and find out. Not to mention you'd be paying a lawyer to have fun trying to keep a straight face. "Judge, the FAA regulates public-use airports and preempts all local regulations. The FAA does not have a rule against landing on the taxiway, grass areas, ramp, or anywhere else on the airport that my client darn well pleases. Therefore, this local ordinance that says airplanes must land on the runway is not only completely ridiculous and unreasonable but also legally unenforceable."