This year started out with the bed having a lot of Creeping Charlie in it. I spent two or three hours hand weeding the entire bed, but by the end of this cool and damp summer the Creeping Charlie (CC) had completely taken over, to the extent that the strawberry plants were not even visible by the end of the summer.

So I guess I'm starting over. One thing I do know is that I want a bed or beds that are narrow enough that I can pick the whole thing without stepping in amongst the plants. But my biggest concern is how to detail with the CC. What I have in mind is a system where I have at least two beds, and every year I dig up the plants in one bed, keep them alive while I Roundup everything left in the bed, and then replant them.

My land is not treated like some suburban lawn, so I also have a problem with crabgrass invading along with the CC. Will using raised beds put an end to that?

Short answer, no. it will be better. They will find it in time
You could put landscaping cloth or plastic over the beds and cut holes and plant strawberries. No runners can take, but no weeds either. You could pot the runners for a new bed later. I would kill all weeds first. Then put cloth over.
This should give you a few years of weed free beds. They will probably find the holes with time. Do it again...
Landscape cloth is better as if put on the right way, water will penetrate. No good answer.

I would not use Roundup in a fruit garden. Some says it is harmless on the soil, but some says it is related to Agent Orange. Whatever, I do not want it in my garden. Dew will probably fight with me on that....

Anyhow, I do not grow strawberry since I can't keep them clean enough. I'll have to buy straw to keep the fruit clean, so this is why is is called strawberry. I could grow them in containers or in raised bed with potting mix...

I can't keep strawberries clean but i grow them all the same. It's a mess, but so good!

The farmer here mounds a row for tomatoes, and cuts an X where he puts plant. You can put a drip line under plastic. Also said you can lay a soaker hose down on top.
The dirt on top keeps the palstic in place. I suspect weeds will grow there though! Roundup!
I myself don't really care that much about toxins, I'm already old, and will be dead before any ever kills me.

OK, well that is Agent Orange (2,4-D). I use it too, same way, just spot treat. Hand pick in garden. i kinda want to buy one of those weed torches. Sounds like a good toy!

I also grow musk strawberries, notice the red seeds.

Daily harvests were great in June!

2,4-D is NOT Agent Orange.
Yes, it was part of AO, along with its more persistent sibling 2,4,5-T; but the big 'danger' of AO was that much of what was used in times past was contaminated with dioxins.
The active ingredients(2,4-D and 2,4,5-T) actually have fairly low toxicity to animal life and fairly short half-lives in the environment; not so for dioxins...

2,4-D is not Agent Orange. Agent Orange is a mix of 2,4-D and 2,4,5-T.

2,4,5-T is a bit more dangerous than 2,4-D, but not hugely so. The big problem with Agent Orange was that the 2,4,5-T was contaminated with 2,3,7,8-tetrachlorodibenzodioxin (TCDD), which is about as toxic as anything can get.

So, again, stop trying to scare people - and if you're not sure about something, or don't understand something, don't post it.

No one says Roundup is Agent Orange. Clearly some components are related.

I only use Roundup to kill tree stumps, some hard-to-kill shrubs and maybe some weeds I can't pull. I do not care if it is Agent Orange, or Agent Green. I just do not use it with my food area.