Fixing a Braided Rug - advice please

Our side entrance is also our mudroom, our laundry room and our coat closet. Having all this together would be really convenient if the room weren't the width of a hallway, and the length of a small bathroom. The current set up might work if there weren't six of us, or if we didn't have outside animals that require us to tromp in mud to care for them. A much larger room for these purposes is at the top of my wish list for when we build.

After moving here, I quickly learned that rugs at the doors were an absolute necessity. Mud is a constant battle. I found some very cheap rugs at Big Lots, one for the laundry room and one for the front door. They are braided, and have lasted well considering the abuse they take at the boots of my family, and the total neglect that they suffer in my care. They are at the point though, that they do need some attention, and I need some advice.

Strips are loose on both of the rugs. They get caught in the doors, which is not only annoying, but makes the problem worse. I know that I could sew them back into the coil, but with what? Do they make special heavy duty needles and thread for this purpose, and if so would purchasing them be worth the investment to fix my Big Lots rugs?

If I do get them sewed up, how on earth do I clean them? The one at the front door cleans up fairly well just with the vacuum. The one at the back door is just full of dirt. The vacuum helps, but the rug is still dirty. They aren't huge rugs, but they are too big for my washer. Any suggestions?

I have often thought about making my own braided rugs from old jeans or other recycled material, but they appear to me very time intensive. For now I need to either make the ones I have work, or I will have to purchase different ones. I'd rather make do with what I have. Any ideas or suggestions?

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Fixing a Braided Rug - advice please + work