I too feed rounds. We do our own, test it, it's stored outside, and have never had a problem. I've been feeding rounds for over 25 years. Never had a horse come up with heaves. I see more heaves from horses barn kept and fed poor two year old rotten hay.
Buy from a reputable grower, that is tested for nutrition, and make sure it's current. Are your bales net wrapped? I feel it helps.
My bales do get the wet yucky spot on the bottom. I roll it around the field, peel it off when I unwrap it and the first top layer. Alls good. Watch for dusty white mold, and smell it for freshness. Flaky light green mixed with stems after peeling off the sun bleached top is ideal.
This year our hay is pretty cruddy, mostly stems due to the bermuda burning up. Going through 1 bale a week for three horses, YUK! But nothing makes me happier than watching them nap on and gorge themselves with it when it's cold or nasty out.