I've carried heavy loads on my trailer. This was probably 300 or 400 lbs, and the cargo bike and trailer aren't light either.
The load really SLOWED ME DOWN. It was hard work even in relatively flat areas.
At some point I get to where it is very difficult for me to pull my trailer up a hill walking. I really needed lower gearing and a trike to allow riding slower than walking.
There are a lot of kid's bike trailers that are designed to connect to the bike, and some of them can do quite well. And, are even lightweight. I've seen some apparent nomadic individuals who adapted wheelchair wheels to their trailer (long wear no flat tires).
I agree, this whole thing sounds tough on the dogs. But, 5 to 10 miles a days is also extremely short. Most bike tourists ride maybe 50 to 100 miles a day.
I'm not sure how you deal with a raw meat diet, or if it is even necessary. One of the differences between the typical domestic dog and wild dogs is the domestic dogs are adapted to metabolize carbohydrates. I don't know about your particular dogs.
Anyway, I'd encourage you to really consider economizing on weight. Perhaps 50 pounds max including the trailer.