I had the same issue a couple of months ago.
I have been playing the Bb clarinet for a couple of years, but felt I was not getting on as well as I might. I struggled to cover some of the holes and had reached a plateau.
My tutor suggested trying the alto sax. He had an ex demo one available, and I had a couple of lessons. I got on surprisingly well. Yes, fingering is different (even now, when playing the middle G I remove all fingers and end up playing a C#) and the octave key only comes in from D upwards, instead of B. However, it is much easier to blow. My tutor said my clarinet playing would help the upper notes, but not the lower notes, and I think he is right. I struggle consistently to get lower D - it tends to go up an octave. I think I try too hard, and with a too tight an embouchure. I ended up buying the ex demo alto!
I must admit I haven't even played the clarinet for the past 2 months - I have been busy playing and transposing some clarinet duets so that I can play with my mum, who still plays the clarinet. There are not too many duets available for clarinet/sax.
Can you have a try out of an alto? I love the sound of the tenor also, but being very petite, I doubted whether I would have handled the tenor. The soprano was too much like the clarinet, and can be difficult to play in tune I understand.
Good luck! If I can help further, please shout 😀 Let us know how you get on.
Miranda