Stats fixes and enhancements

[ejolly]

These are bug-fixes but many are enhancements that would be likely candidates for moving into burnt-ends. We had also discussed creating a stats output class #172 which should be straightforward using the new Python dataclass decorator.

Relevant issues:

• [ ] #182
• [ ] #183
• [ ] #172
• [ ] #176
• [ ] #177
• [ ] #148
• [ ] #244
• [ ] #304
• [ ] #315
• [ ] #345
• [ ] #354
• [ ] #287
• [x] #417
• [ ] #395
• [ ] #410
• [ ] #418