Whilst the experimental subjects and data collection are inherently fraught with difficulty, there's still a LOT of low-hanging fruit regarding things like automation. Many scientists use computers to write up results, to store data and perform calculations, but there's often a lot of manual, undocumented work which could easily be scripted to help those re-running the experiment. For example, running some program to produce a figure, without documenting what options were used; providing a CSV of data, without the formulas used for the aggregate statistics; relying on a human to know that the data for "fig1.png" comes from "out.old-Restored_Backup_2015~"; etc.
Such scripting is a step on the path to formalising methods. They'd help those who just want to see the same results; those who want to perform the same analysis using some different data; those who want to investigate the methods used, looking for errors or maybe doing a survey of the use of statistics in the field; those who want a baseline from which to more thoroughly reproduce the experiment/effect; etc.
The parent's list of mouse-frighteners reminds me of the push for checklists in surgery, to prevent things like equipment being left inside patients. Whilst such lists are too verbose for a methods section (it would suffice to say e.g. "Care was taken to ensure the animals were relaxed."), there's no reason the analysis scripts can't prompt the user for such ad hoc conditions, e.g. "Measurements should be taken from relaxed animals. Did any alarms sound in the previous 24 hours? y/N/?", "Were the enclosures relatively clean? Y/n/?", "Were the enclosures cleaned out in the previous 24 hours? y/N/?", etc. with output messages like "Warning: Your answers indicate that the animals may not have been relaxed during measurements. If the following results aren't satisfactory, consider ..." or "Based on your answers, the animals appear to be in a relaxed state. If you discover this was not the case, we would appreciate if you update the file 'checklist.json' and send your changes to 'experimentABC@some-curator.org'. More detailed instructions can be found in the file 'CONTRIBUTING.txt'"