Lots of cool ideas, but I’m not sure how possible they are myself 
There’s some that I know people have attempted before, so I know they’re definitely somewhat possible, and you might want to look at them for inspiration.
Have you looked at the Archipelago Mod yet? It has a fisher class, and if it’s not set up how you want, it might still be worth looking at.
This mod had its cart act like any other storage item. However, some model settings when the item was carried could have made it look like it was properly being pushed. I’d still love to see an overhaul hehe of hauling like you suggest rather than just visual touches, though.
You might have already seen the Brewery mod, but it might be good inspiration to build off of - it would be cool to see drinks with buffs and debuffs again, though I don’t know how much further you’re wanting to take your brewing.