When I planned these beds I spaced them far enough apart to get my lawn tractor in-between them, but getting between them and the fence involved my weed whacker. As anyone with a fence has found out, maintaining the grass at the base of a fence is a pain.
I'm 3/4 of the way done with the edging. It's 10" tall with something like 6" or 7" of it buried. It does a good job of keeping grass out of our other beds, so I'm sure it will do a good job here. The downside is the most effective way of installing it is to trench first, put the edging in, and then refill the trench. If you try to use one of those big pizza peel looking things to make a narrow slide the will usually get wavy due to variation in trench depth.
I mowed to basically ground height between the beds, weed whacked around the beds, and put in a layer of that thick paper builders will use to protect flooring below the mulch. Some areas for cardboard instead, but we just didn't have enough cardboard to cover it all. Hopefully it will be enough to kill the grass and hopefully that results in less grass appearing in my raised beds.
We might expand for more beds once our kids outgrow their play structure. We have four 4x8 beds and grow vertically, so we have a decent amount of space. This year we have beans, peas, cucumber, cantaloupe, trombetta, pie pumpkins, shallots, onions, carrots, tomatoes, eggplant, peppers, and lufa for fun.