I agree with the comments that going to a wheel with more spokes is better than increasing the spoke gauge. We had problems on our tandem that we used for both commuting and loaded touring with just a rear rack carrying all our stuff. Tried progressively thicker spokes and they just started breaking even earlier (I suspect the thicker gauges had poorer quality). Then went to a 48 spoke wheel with butted 14/15 gauge spokes and didn't have any more problems. You have much less of a load than we did so I'd expect a 36 or 40 spoke wheel should be adequate.

Am a bit puzzled by your comment about 2-wheel trailers. I've frequently had my Bike Friday 2-wheel trailer over 50 mph on downhills with no issues at all. How fast are you planning on going that would make one "too unstable at the speeds I ride?" But I doubt that the BoB trailer is a major contributor to your spoke issues.