So after a lot of iterations and experimentation, this is where I ended up! I'm a lot more satisfied with this design, than I was with how I previously drew him. I'm sure he'll change over time, but I think this is a big improvement. Also, I'm entering Pubby into a character design contest, so I figured I'd made a new turnaround for him.
And these were some initial sketches of Pubby that I did to really experiment and figure out how I wanted him to look.