Ways for science as an academic institution, or for you personally? For the latter, Luke has already done the work of creating a post on that. For the former, it’s more difficult, since a lot of productivity in science requires cooperation with the existing institution. At the least, I would suggest registering your experiments in a public database before conducting them, if any exist within your field, and using Bayesian probability software to process the statistics of your experiments (this will probably not help you at all in getting published, but if you do it in addition to regular significance testing, it should hopefully not inhibit it either.)
Ways for science as an academic institution, or for you personally? For the latter, Luke has already done the work of creating a post on that. For the former, it’s more difficult, since a lot of productivity in science requires cooperation with the existing institution. At the least, I would suggest registering your experiments in a public database before conducting them, if any exist within your field, and using Bayesian probability software to process the statistics of your experiments (this will probably not help you at all in getting published, but if you do it in addition to regular significance testing, it should hopefully not inhibit it either.)