Taking care of a flower bed. So calm down and take a deep breath. I think you are overestimating how difficult it is to maintain a flower bed that is properly set up. I have a few suggestions to make this flower bed much more maintenance free than the grass.
You want to plant grass early so it gets developed before the heat of the summer.
- Start with a bed that doesn't have weeds. This bed is probably too far gone to save. I would pull out your favorite plants and use roundup on all of the rest. The roundup will state on the bottle how long you need to wait before planting. There are several that are only 1 day of waiting time like the one linked below.
- You need to have good boarders to help maintain a barrier between the grass and flower bed. Rocks do not make good boarders because they do not prevent grass from creeping under them. Check out the double brick boarder that I linked below. If you dig down a bit and have sand under this boarder the grass will never get into your landscape. It also prevents the mulch from getting into your lawn. This boarder is also nice because your flowers can hang over without getting in the way of the mower. There are other boarders like this but the idea is to have it deep enough to prevent grass from being able to run under. Get a good 3" of mulch in there and you will find that you have much less of an issue with weeds. You probably never mulched heavily before because it would fall out because of your boarder problem.
- Always use a pre-emergent weed preventer like Preen early in the Spring to prevent weeds. Combine this with the mulch and your weeding time will be less than mowing the area by far.
- Plant native perennial plants in your bed.These will generally require less maintenance and watering. If you get 4-6 hours of direct sunlight then plant shaded plants. 6 hours will work for full sunlight plants. The sun is not strong in the morning so sunlight time before 9:00 AM is negligible.
- Put down a high quality tarp under the mulch to further prevent weeds.
The method of edging you linked will work but it's not very good at keeping the mulch in your flower bed and you will have to redo the edge multiple times each year so it does not fill back in. I've seen people use this method on on the outside of rubber tube edging and that seems to be effective.