As far as gerrymandering, what constitutes fair districting anyway? It may be easy to spot egregious gerrymandering, but how do you select best map among myriad of possible maps that are not overtly gerrymandered? There is no one best solution. I think the best solution is to just get rid of districts altogether and have proportional representation. That would also allow minor parties to be represented without them acting as spoilers.
We do know how to create non-gerrymandered electorates.
1. Electorates based solely upon population i.e. each electorate has
N voters +/- %
N. Don't base the number or boundaries upon age, colour, creed, previous voting or any other such category.
2. Regularly review the electorates' boundaries. I think you Yanks do it every 10 years after your census. If so, that is too far apart. Make it, say, 5 years to more accurate reflect population changes. We do it every 3-4 years after each state or Commonwealth election.
3. An independent electoral commission. Do not let pollies or political parties draw the boundaries. The only criteria for the boundaries is population. (This is the one you probably cannot manage).
4. Standardise counting and ballot marking procedures. Having paper, electronic systems, (bloody) chads intermixed is a recipe for trouble.
4. Get more people to vote. Your voting rates are abysmal.