It’s hard to pinpoint without watching a hearing you. I don’t think it’s the mouthpiece. Regarding reeds, don’t worry about the different sizes as much as trying different reeds. Each reed is different, even from the same box so just keep to the strength that is comfortable for you to play. Get the full box of reeds into a glass of water so they’re about half covered for 5 minutes then play each one and see if they all do it or not. This test will let you know if it’s a reed problem or not, then you can carry on from there. Let me know how it goes!
Also don’t adjust your lig too tight as this will choke the reed.
Check my video on reeds in the “Tips” section of the lessons.
Johnny