At this point, I wouldn't even bother trying to convince him to stay let alone consider offering the supermax. Kawhi and his camp's at ude isn't gonna change anytime soon.
Trading him now is the best option imo. The Spurs don't necessarily have to give him what he wants and send him to LA. If he refuses to sign an extension with whichever team he gets traded to, he will lose a 30M more in guaranteed money on top of the 50M he's lost by not getting the supermax iirc. It wont be easy to make that money back in sponsorship deals even in a large market.
The Celtics, Lakers, Clippers, Kings, and Sixers are all rumored to be interested. A lot of people are expecting the Spurs to get lowball offers but there are angles that could work in the Spurs favor. The Clippers, Lakers and Celtics hate each other, lowballing could send Kawhi to their rivals. The Celtics own the Kings 2019 pick (its protected iirc), but if the Kings get Kawhi, they could also get that pick back from Boston. The Celtics are already contenders but if the Sixers get Kawhi, that's another team theyd have to get past in the East.
Bottom line, losing Kawhi sucks but we have options.