You didn't mention if your plants flowered and if they did but still didn't produce cucumbers, the problem would be lack of pollination. Pollination is mainly done by bees as other insects are generally ineffective. In urban settings, it is not unusual to have a lack of bees.

When no bees are present in the garden or the bee population is too low for good fruit set, you could pollinate by hand. It's a tedious chore, but it is the only means of obtaining fruit set in the absence of bees. The pollen is yellow and produced on the structure in the center of the male flower. You can use a small artist’s paint brush to transfer pollen or you can break off a male flower, remove its’ petals to expose the pollen-bearing structure and roll the pollen onto the stigma in the center of the female flower. When hand pollinating, it is important to use only freshly opened flowers. Flowers open early in the morning and are receptive for only one day.

Soil testing is ideally done in the spring prior to seeding or planting time, however, it may be more practical to test soil in the fall when soil is dry and there are fewer time constraints.   Unfortunately, summer or fall samples can only tell us the current nutrients in the soil at the present time. You apparently had enough nitrogen at planting time but N moves rather quickly through the soil and your spring N has probably been depleted by now. That could be why your soil test shows a need for nitrogen.

Soil test results can be confusing to understand. If you are unsure of what your report means, I suggest you contact your local extension office. For further reading about soil test results, go to this link: http://www.extension.umn.edu/garden/yard-garden/soils/soil-test-interpretations-and-fertilizer-manag...

Regarding the nitrogen in your soil:  you apparently had plenty of nitrogen at the beginning of the season but by this time of year it has been depleted.  You would normally only add nitrogen in the spring.

Yes, the weed control spray has a very detrimental effect on the bee population and that's one reason why we see less bees in an urban setting.

I could not find any research giving a reason for lack of fruit set specifically in Asian cucumbers other than the general ones I mentioned.  I would suggest that you apply less nitrogen next spring than you did this year as too much top growth inhibits fruit set.  Inadequate pollination - mainly by bees - is the other concern.