My favorite way to fish.  You're going to have a blast.

For reference, I'm smaller but close to your size.  I use a Hala Fame for 90% of my SUP fishing.  It's very stable and holds a ton of weight at 11'3x6"×36".  It drifts rivers well, check out it's "stompbox".  Its still easy to put in miles paddling large lakes or the Columbia.  Hala has welded seams and a 5 year warranty.  Be sure to look at that when you compare the Fame to other SUPs.  If you want to try it for a paddle let me know and we can probably make it happen.

Just one negative to balance out all the positive, in my opinion the scotty mounting pads are in the wrong location on the current model.

https://halagear.com/products/fame


Check the photos in the AOTY SUP division if you want to see how fishy it is.

Good luck on your search.  For your size, I'd recommend not going smaller than 11'x6"×34" if you're looking for stability.