How to raise and maintain happiness levels without shutting down the economy?
Solution 1:
Decorations
Firstly, build a few decorations where they are most of the time, such as when idle; in rooms as you've already done, but also in communal places where they like to idle. The market is usual, maybe a balcony if you have one, or the tavern. In this way when they idle they get happiness from idling, and also from being near fancy items. Placing the items where they are most of the time is the best way to get more bang for your buck, of course you can decorate all areas to improve their happiness generally.
Fixing low happiness
What makes them happy the most is idling. My problem was that when I first started I'd start loads of building projects, immediately starting the next one once the last had finished. I generally set the auto-production levels too high, meaning the townies always had something to do. This resulted in townies being unhappy, meaning when they died they wouldn't get replaced, resulting in more work for those left, meaning more unhappy townies. It can be a downward spiral.
To get out of this firstly, let them finish up any extra work, like building walls, decorations etc.
Then change your automatic production to the minimum needed, e.g. only food and only a little food. In my town I went for farming cows and chickens, starting out i only automatically butchered one of each, and cooked one of each. I also produced one egg and one milk pale, but that was it. This way you're doing the minimum to survive. They only make a food item if there are none left. Note that your heros might not like this (they might leave due to lack of food), but once your happiness is sorted out and your economy is back on track the heros will easily come back.
Monitor this a bit, ensuring you are producing enough food, what you should find is that you won't hold much stock, but when hungry the townie will either go and make some food, grab one just prepared, or if you're not producing enough food generally they'll go and get raw food, e.g. milk/eggs.
Economic growth vs. happiness
Hauling does count as a job as you say, so whenever I'm ready to explore a new dungeon level or take on a lot of mining etc. that will mean lots of traveling around carrying things I try and stop most building work beforehand to get them starting as happy, well fed, rested etc.
Don't worry about the fact that to start with you are only dealing with basic materials and items. Progressing down the dungeon layers for better items is a big job. You really want happiness to be high when you go down a layer as townies like running into a raging battle to collect some bones (for example). You want a stream of villagers ready to replace them if this happens which you get if everyone is happy.
They key is as long as they are happy you will have a good economy as its easy to get more townies (just build more rooms), so that is the priority not economy (beyond food).
Town design
I also try and design my towns so the distance from food source to dining room is as minimal as possible. I have lots of farms (cows and chickens in my case as they give milk and eggs in addition to meat) and a kitchen right next to them, then a dining room right next to that (with walls/doors in-between so it looks nice). The point is to minimize the time taken to do repetitive tasks, making/preparing/eating food is the main one.
The same goes for any production chain, although obviously some things you can't control the location of, for example sources of metals.
I tend to have any barrels of stock in a central location that's fairly near to anything that would need them, i.e. raw/prepared food barrels in the kitchen, stone in the masonry area etc. This way things get moved most of the way in one go.