Small jet Captain reported encountering severe turbulence at FL400 that resulted in an inflight upset. Control was regained and smoother air was found at a lower altitude.

Narrative

After takeoff from TRM local ATC vectored us around for a few minutes and then handed us off to LA center who handed us off to Joshua Tree. The Controller cleared us direct to BTG. We had filed a flight plan that would've avoided the SIGMET box along our filed route however the Controller advised us that that SIGMET was no longer a factor and that it had 'cleared itself out' and that we would experience a good ride.As we neared the area of the SIGMET; I noticed that it was elongating and that the winds were increasing in strength. The wind at our position prior to the incident was from the west at 91 kt. I directed the first officer to ask for a heading change that would avoid the end of the lenticular type cloud; but we were unable to immediately contact Joshua Tree. After a few tries; we were finally given a turn of 30°. I then directed the first officer to ask for another 30° and to advise and that we would need a re-route over central California. However; we hit the severe turbulence moments later and the airplane became extremely unstable. The first officer asked ATC for a lower altitude and we were given a descent to 38;000 feet followed by a descent to 36;000 feet. Leaving 36;700 feet the turbulence subsided and the ride was smooth from that point on.ATC queried us as to damage to the aircraft or injuries to occupants and we advise that there were none known. I then contacted our Director of Operations to ask his advice on continuing to ZZZ. We discussed the state of the aircraft and as there were no adverse control reactions we decided to continue on to ZZZ. The rest of the flight was uneventful and we landed without further incident.I don't know if a more timely response from ATC would've helped us to avoid this situation. However; if I had not accepted the direct routing and stayed on our filed route of flight; my consensus is that the severe event may not have happened. I made the mistake of trusting what the Controller said and should have looked at what was ahead in print.