If you want something a little simpler, there are carts out there that are basically just a seat on wheels.
For just carting/drafting not carrying a person, you can get a beginner's type 2-wheeled cart for a fairly low price, or a nicer one for a little bit more.
I did some carting with my Golden Retriever, a friend of mine built her a cart out of wood but it ended up being really heavy. I went to dog camp with my GSD a few years ago and they had a carting trainer and he was able to give us a short lesson, and Bianca had never done carting before so I wasn't sure how far we'd get. However in that short time, it was maybe 30-45 minutes, we went from her never having seen a cart before, introduced the harness, introduced the cart and actually had her pulling the cart on her own during that time! Of course we went through each step you would normally go through (just putting the harness on, showing her the cart, having her walk next to the cart, hooking her up, having her walk with the cart behind her but not pulling it, having her pull it but with us holding it, etc...) but she breezed through each one so quickly and was so comfortable with it that we were able to get her from zero to pulling the cart in that short lesson. So it may not take as long as you think to train them, depending on the dog's personality and comfort level. My Golden I went slowly, introducing her to the cart, having her pull milk jugs and so on like the "Intro to Carting" site's instruction say. Of course you also have to train the commands for slow down/speed up, go, stop, and turns after that, but I always teach my dogs commands that mean to slow down, speed up and stop anyway even without the carting so I pretty much just need to add the left/right turns...
One thing about having you in the wagon, you will have to do a lot more training if you want to actually do "driving" because they will be on their own without you holding a leash and walking with them to guide them along. I also found my Golden didn't like to pull if I was behind her, I think it was because her training to not pull on the leash was so ingrained so she would only pull the cart if I was next to her or in front of her.
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Jubal/Tesla (Beauceron) 3/14/14
Bianca HIC CGC TT (GSD) 4/24/04-10/23/12