There is a real contradiction in the OP's statement. The clarinet embouchure requires a great deal more exertion and muscle strength than any of the saxophone embouchures because the clarinet plays at the top of its mouthpiece pitch. That would normally translate to a clarinet player being able to play for longer periods on the tenor sax than on the clarinet before embouchure muscle fatigue kicks in.
Some clarinet players have learned to play by using the body of the clarinet as a "lever" pulling it down to put pressure on the lower lip. Using this technique inhibits the strengthening of the muscles around the mouth which form the embouchure. I'm not saying that the OP plays the clarinet this way, but it would offer an explanation for the contradiction.
I would advise against going to a softer reed than a Rico Royal 2 1/2 on a Selmer C* which is an excellent "middle of the road" combination. Instead I would recommend playing long tones daily, checking the pitch of the mouthpiece and crook to make sure it is no higher than an E concert, and to do Larry Teal's smile-whistle-smile-whistle 50 times exercise several times a day. In a week or so the problem will take care of itself.