The only time I've ever seen negative results published is if someone tries to repeat "known" science, fails to do so, but finds something interesting in the mean time.
I used to hear these complaints about negative results in chemistry. The problem is, most scientific experiments (including clinical trials) are negative. If published, you'd need to increase the number of papers by ~500% to include all these failed experiments.
The best idea I've had is to minimize effort for negative experiments. Like arxiv, but perhaps a even less formal. Allow it to be easily searchable. It's still not incentivized, but it's a fuckton easier to put it out there.
I could also see dedicated data analysts publishing negative data of open data sets.