Good job with the new farm. I just moved this season about 1300 km south from where I use to live, and I got into a colder zone 6B with the elevation, about 510 meters :)
The harrow tool you showed for the weeds is generally used only on the young plants for a couple of weeks. One suggestion, you may want to look into hoop houses or green houses. You can easily add a month or two to your normal grow season with them. If you add row covers inside you can easily add more weeks.
I moved here the end of July, and grew a few Jade bush beans. They recently got hit and killed by frosts. Now just growing cover crops of field peas, rye grass, hairy vetch and crimson clover. I double dug one bed , the next bed just flipped the soil, last bed laid down
cardboard with some mulch (all beds 1 x 7.6 meter). Started a 7.6 x 7.6 meter bed area also with cardboard on the
lawn. I planted some garlic and fava beans. I also got a free truck delivery of shredded
trees, and will get another some day in future?
Carrots, Brussels sprouts, kale often taste sweeter when these plants get some frost. Great idea to focus on onions, beets, carrots, minzuna, and lettuce varieties. Bush beans have roughly a 55 day maturity so might be able to grow there. Funny when you said you tried with the shorter beans. Maybe try peas, they are more cold tolerant than beans.